No / This paper presents a novel approach for probabilistic clustering, motivated by a real-world problem of modelling driving behaviour. The main aim is to establish clusters of drivers with similar journey behaviour, based on a large sample of historic journeys data. The proposed approach is to establish similarity between driving behaviours by using the Kullback-Leibler and Jensen-Shannon divergence metrics based on empirical multi-dimensional probability density functions. A graph-clustering algorithm is proposed based on modifications of the Markov Cluster algorithm. The paper provides a complete mathematical formulation, details of the algorithms and their implementation in Python, and case study validation based on real-world data.

Doctor of Philosophy / Department of Mathematics / Ivan Blank / Under the guidance of Dr. Ivan Blank, I study the obstacle problem with an elliptic operator in divergence form. First, I give all of the nontrivial details needed to prove a mean value theorem, which was stated by Caffarelli in the Fermi lectures in 1998. In fact, in 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for elliptic operators in divergence form with bounded measurable coefficients. The formula stated by Caffarelli is much simpler, but he did not include the proof. Second, I study the obstacle problem with an elliptic operator in divergence form. I develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results allow us to begin the study of the regularity of the free boundary in the case where the coefficients are in the space of vanishing mean oscillation (VMO).

By an orthodox application of the perturbation theory to the general case of a quantized field, it is shown that the divergence difficulty hitherto encountered arises from a faulty application of the expansion method. The difficulty disappears if the degeneracy of the unperturbed system is properly treated by the method of secular perturbation. Physically, it is shown that this amounts to a rigorous treatment of the radiation reaction.

Philosophiae Doctor - PhD / Variation in sympatric and allopatric populations is believed to be a precursor to eventual speciation. The dispersion of genes from one gene pool into another is prevented by various processes, including the founder effect, sexual selection, ecological differences and random genetic divergence. Examining patterns of intraspecific variation in phenotypic and genotypic traits may thus provide valuable insights into the processes that govern species origination. Bladder grasshoppers (Orthoptera; Pneumoroidea) are an ideal model system to investigate patterns of geographic and ecological divergence due to their high host plant specificity, low dispersal and distinctive acoustic signals. This dissertation investigates intraspecific diversification in the bladder grasshopper Bullacris unicolor (Orthoptera: Pneumoroidea). Recent research on this species has shown significant intra- and inter-population variation in male advertisement calls and morphological characters. However, the exact cause of this variation has remained unclear. Furthermore, a previous study showed that the calls of B. unicolor from one particular population are highly differentiated from other populations, possibly due to the effects of anthropogenic noise. Here we aim to examine the drivers of diversity within Bullacris unicolor by embracing a multidisciplinary approach that encompasses the effects of environmental factors, genetics, anthropogenic noise and host plant associated divergence.

With the huge amount of subjective contents in on-line documents, there is a clear need for an information retrieval system that supports retrieval of documents containing opinions about the topic expressed in a user’s query. In recent years, blogs, a new publishing medium, have attracted a large number of people to express personal opinions covering all kinds of topics in response to the real-world events. The opinionated nature of blogs makes them a new interesting research area for opinion retrieval. Identification and extraction of subjective contents from blogs has become the subject of several research projects. In this thesis, four novel methods are proposed to retrieve blog posts that express opinions about the given topics. The first method utilizes the Kullback-Leibler divergence (KLD) to weight the lexicon of subjective adjectives around query terms. Considering the distances between the query terms and subjective adjectives, the second method uses KLD scores of subjective adjectives based on distances from the query terms for document re-ranking. The third method calculates KLD scores of subjective adjectives for predefined query categories. In the fourth method, collocates, words co-occurring with query terms in the corpus, are used to construct the subjective lexicon automatically. The KLD scores of collocates are then calculated and used for document ranking. Four groups of experiments are conducted to evaluate the proposed methods on the TREC test collections. The results of the experiments are compared with the baseline systems to determine the effectiveness of using KLD in opinion retrieval. Further studies are recommended to explore more sophisticated approaches to identify subjectivity and promising techniques to extract opinions.

With the huge amount of subjective contents in on-line documents, there is a clear need for an information retrieval system that supports retrieval of documents containing opinions about the topic expressed in a user’s query. In recent years, blogs, a new publishing medium, have attracted a large number of people to express personal opinions covering all kinds of topics in response to the real-world events. The opinionated nature of blogs makes them a new interesting research area for opinion retrieval. Identification and extraction of subjective contents from blogs has become the subject of several research projects. In this thesis, four novel methods are proposed to retrieve blog posts that express opinions about the given topics. The first method utilizes the Kullback-Leibler divergence (KLD) to weight the lexicon of subjective adjectives around query terms. Considering the distances between the query terms and subjective adjectives, the second method uses KLD scores of subjective adjectives based on distances from the query terms for document re-ranking. The third method calculates KLD scores of subjective adjectives for predefined query categories. In the fourth method, collocates, words co-occurring with query terms in the corpus, are used to construct the subjective lexicon automatically. The KLD scores of collocates are then calculated and used for document ranking. Four groups of experiments are conducted to evaluate the proposed methods on the TREC test collections. The results of the experiments are compared with the baseline systems to determine the effectiveness of using KLD in opinion retrieval. Further studies are recommended to explore more sophisticated approaches to identify subjectivity and promising techniques to extract opinions.

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This dissertation addresses the task of learning to rank, both in the supervised and unsupervised settings, by exploiting the interplay of convex functions, monotonic mappings and their fixed points. In the supervised setting of learning to rank, one wishes to learn from examples of correctly ordered items whereas in the unsupervised setting, one tries to maximize some quantitatively defined characteristic of a "good" ranking. A ranking method selects one permutation from among the combinatorially many permutations defined on the items to rank. Accomplishing this optimally in the supervised setting, with minimal loss in generality, if any, is challenging. In this dissertation this problem is addressed by optimizing, globally and efficiently, a statistically consistent loss functional over the class of compositions of a linear function by an arbitrary, strictly monotonic, separable mapping with large margins. This capability also enables learning the parameters of a generalized linear model with an unknown link function. The method can handle infinite dimensional feature spaces if the corresponding kernel function is known. In the unsupervised setting, a popular ranking approach is is link analysis over a graph of recommendations, as exemplified by pagerank. This dissertation shows that pagerank may be viewed as an instance of an unsupervised consensus optimization problem. The dissertation then solves a more general problem of unsupervised consensus over noisy, directed recommendation graphs that have uncertainty over the set of "out" edges that emanate from a vertex. The proposed consensus rank is essentially the pagerank over the expected edge-set, where the expectation is computed over the distribution that achieves the most agreeable consensus. This consensus is measured geometrically by a suitable Bregman divergence between the consensus rank and the ranks induced by item specific distributions Real world deployed ranking methods need to be resistant to spam, a particularly sophisticated type of which is link-spam. A popular class of countermeasures "de-spam" the corrupted webgraph by removing abusive pages identified by supervised learning. Since exhaustive detection and neutralization is infeasible, there is a need for ranking functions that can, on one hand, attenuate the effects of link-spam without supervision and on the other hand, counter spam more aggressively when supervision is available. A family of non-linear, iteratively defined monotonic functions is proposed that propagates "rank" and "trust" scores through the webgraph. It relies on non-linearity, monotonicity and Schurconvexity to provide the resistance against spam. / text

For almost every organism there are large gaps in our knowledge about the processes that leads to speciation. The changes an organism undergoes before divergence has occurred have remained a mystery, as it is difficult to say whether or not a species is going to diverge and when. To investigate this unknown the European whitefish (Coregonus lavaretus) and the northern pike (Esox lucius) were studied, as they produce a repeatable and predictable pattern of speciation in sympatry. To investigate the changes in phenotypes and behaviour in whitefish that precedes divergence, two lake populations were examined, Gräsvattnet and Ringsjön. Gräsvattnet was used as a control, with a population of whitefish but an absence of pike, whereas Ringsjön has a population of whitefish that invaded from Gräsvattnet and a pike population. The presence of pike presumably exerts divergent selection on the whitefish population. Fish and zooplankton were surveyed in both lakes from 1970 to the present day, which allows us to compare how whitefish populations and their resources change in the presence and absence of pike. The results found in Ringsjön show; (1) a change in habitat use, (2) a change in diet from pelagic to benthic, (3) an increase in the relationship between individual body size and diet and (4) a decrease in average size over the course of the study. (1)The presence of pike is believed to have forced the whitefish into the pelagic which could be seen in the result, with an increase in individuals caught in the pelagic. (2) The change in diet is thought to be caused by a resource competition created by individuals being forced to use the pelagic. Although insignificant this led to an overall reduction in zooplankton abundance by almost 40% which could have intensified competition. The resource competition could then have been intensified further by the change in composition of zooplankton relative abundance. (3) The increase in relationship between individual body size and diet is thought to increase due to the resource competition between smaller and larger individuals in the pelagic. Smaller individuals are better competitors than larger individuals for pelagic resource which could have led to the larger individuals switching to a more benthic diet. (4) The decrease in average size is thought to be caused by negative selection for larger individuals. Larger individuals have switched to a more benthic diet, and although the individuals are larger they still face the risk of predation in the littoral zone as they have not outgrown the gape size of the pike. This could have led to the average size reduction that may be the first steps in speciation, and ultimately leading to the divergence of two morphs by sympatric speciation in Ringsjön. In Gräsvattnet over the course of the study there were few and small changes in whitefish size, zooplankton relative abundance in the diet and in the environment. The results in Gräsvattnet could however suggest resource competition for benthic resources. Although resource competition is thought to be an important factor in the speciation of whitefish, without predation pressure no speciation occurs. This result could suggest the importance of predation pressure in the speciation of whitefish.

The mechanisms behind speciation have been subject of debate for centuries. The presence of resource polymorphism has been discovered to play a significant part in this process, and has been proven to induce phenotypic and genetic divergence. Although resource polymorphism has been intensely studied during the last few decades, there is a gap of information as to why this can be observed in some systems but not in others. Recent studies of European whitefish (Coregonus lavaretus) in Scandinavian lakes have shown that predation, in this case by Northern pike (Esox lucius), could be the factor that induces resource polymorphism. European whitefish is known to diverge into several ecomorphs in Scandinavian lakes, but only in the presence of pike. Divergence is assumed to be caused by the size selectivity of pike, and the following niche separation and eventually reproductive isolation. In this study, pike prey selectivity was studied in the field through sample fishing using hooks baited with whitefish of different sizes. The hypothesis was that pike prefers smaller prey over larger and mainly hunts in the littoral zone. This should causes smaller whitefish ecomorphs to be prone to predation in the littoral and thus utilize refuge spawning grounds with low predation pressure. However, no pike were caught on whitefish spawning grounds, and fishing at two additional pike rich sites displayed a preference towards medium-sized whitefish (p < 0.05). This indicates a size selectivity, although further and improved studies would be required to answer the question of the pike’s role in resource polymorphism.