Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Computational Techniques for Haplotype Inference and for Local Alignment Significance

This thesis which consists of an introduction and four peer-reviewed original publications studies the problems of haplotype inference (haplotyping) and local alignment significance. The problems studied here belong to the broad area of bioinformatics and computational biology. The presented solutions are computationally fast and accurate, which makes them practical in high-throughput sequence data analysis. Haplotype inference is a computational problem where the goal is to estimate haplotypes from a sample of genotypes as accurately as possible. This problem is important as the direct measurement of haplotypes is difficult, whereas the genotypes are easier to quantify. Haplotypes are the key-players when studying for example the genetic causes of diseases. In this thesis, three methods are presented for the haplotype inference problem referred to as HaploParser, HIT, and BACH. HaploParser is based on a combinatorial mosaic model and hierarchical parsing that together mimic recombinations and point-mutations in a biologically plausible way. In this mosaic model, the current population is assumed to be evolved from a small founder population. Thus, the haplotypes of the current population are recombinations of the (implicit) founder haplotypes with some point--mutations. HIT (Haplotype Inference Technique) uses a hidden Markov model for haplotypes and efficient algorithms are presented to learn this model from genotype data. The model structure of HIT is analogous to the mosaic model of HaploParser with founder haplotypes. Therefore, it can be seen as a probabilistic model of recombinations and point-mutations. BACH (Bayesian Context-based Haplotyping) utilizes a context tree weighting algorithm to efficiently sum over all variable-length Markov chains to evaluate the posterior probability of a haplotype configuration. Algorithms are presented that find haplotype configurations with high posterior probability. BACH is the most accurate method presented in this thesis and has comparable performance to the best available software for haplotype inference. Local alignment significance is a computational problem where one is interested in whether the local similarities in two sequences are due to the fact that the sequences are related or just by chance. Similarity of sequences is measured by their best local alignment score and from that, a p-value is computed. This p-value is the probability of picking two sequences from the null model that have as good or better best local alignment score. Local alignment significance is used routinely for example in homology searches. In this thesis, a general framework is sketched that allows one to compute a tight upper bound for the p-value of a local pairwise alignment score. Unlike the previous methods, the presented framework is not affeced by so-called edge-effects and can handle gaps (deletions and insertions) without troublesome sampling and curve fitting.

Efficient search for statistically significant dependency rules in binary data

Analyzing statistical dependencies is a fundamental problem in all empirical science. Dependencies help us understand causes and effects, create new scientific theories, and invent cures to problems. Nowadays, large amounts of data is available, but efficient computational tools for analyzing the data are missing. In this research, we develop efficient algorithms for a commonly occurring search problem - searching for the statistically most significant dependency rules in binary data. We consider dependency rules of the form X->A or X->not A, where X is a set of positive-valued attributes and A is a single attribute. Such rules describe which factors either increase or decrease the probability of the consequent A. A classical example are genetic and environmental factors, which can either cause or prevent a disease. The emphasis in this research is that the discovered dependencies should be genuine - i.e. they should also hold in future data. This is an important distinction from the traditional association rules, which - in spite of their name and a similar appearance to dependency rules - do not necessarily represent statistical dependencies at all or represent only spurious connections, which occur by chance. Therefore, the principal objective is to search for the rules with statistical significance measures. Another important objective is to search for only non-redundant rules, which express the real causes of dependence, without any occasional extra factors. The extra factors do not add any new information on the dependence, but can only blur it and make it less accurate in future data. The problem is computationally very demanding, because the number of all possible rules increases exponentially with the number of attributes. In addition, neither the statistical dependency nor the statistical significance are monotonic properties, which means that the traditional pruning techniques do not work. As a solution, we first derive the mathematical basis for pruning the search space with any well-behaving statistical significance measures. The mathematical theory is complemented by a new algorithmic invention, which enables an efficient search without any heuristic restrictions. The resulting algorithm can be used to search for both positive and negative dependencies with any commonly used statistical measures, like Fisher's exact test, the chi-squared measure, mutual information, and z scores. According to our experiments, the algorithm is well-scalable, especially with Fisher's exact test. It can easily handle even the densest data sets with 10000-20000 attributes. Still, the results are globally optimal, which is a remarkable improvement over the existing solutions. In practice, this means that the user does not have to worry whether the dependencies hold in future data or if the data still contains better, but undiscovered dependencies.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Using Mathematical Morphology for Geometric Music Retrieval

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki.

Phylogeography and Population Genetics of the Moor frog (Rana arvalis Nilsson) in Northern Europe

The ongoing climate change along with increasing levels of pollutants, diseases, habitat loss and fragmentation constitute global threats to the persistence of many populations, species and ecosystems. However, for the long-term persistence of local populations, one of the biggest threats is the intrinsic loss of genetic variation. In order to adapt to changes in the environment, organisms must have a sufficient supply of heritable variation in traits important for their fitness. With a loss of genetic variation, the risk of extinction will increase. For conservational practices, one should therefore understand the processes that shape the genetic population structure and also the broader (historical) phylogenetic patterning of the species in focus. In this thesis, microsatellite markers were applied to study genetic diversity and population differentiation of the protected moor frog (Rana arvalis) in Fennoscandia from both historical (evolutionary) and applied (conservation) perspectives. The results demonstrate that R. arvalis populations are highly structured over rather short geographic distances. Moreover, the results suggest that R. arvalis recolonized Fennoscandia from two directions after the last ice age. This has had implications for the genetic structuring and population differentiation, especially in the northernmost parts where the two lineages have met. Compared to more southern populations, the genetic variation decreases and the interpopulation differentiation increases dramatically towards north. This could be an outcome of serial population bottlenecking along the recolonization route. Also, current isolation and small population sizes increase the effect of drift, thus reinforcing the observed pattern. The same pattern can also be seen in island populations. However, though R. arvalis on the island of Gotland has lost most of its neutral genetic variability, our results indicate that the levels of additive genetic variation have remained high. This conforms to the conjecture that though neutral markers are widely used in conservation purposes, they may be quite uninformative about the levels of genetic variation in ecologically important traits. Finally, the evolutionary impact of the typical amphibian mating behaviour on genetic diversity was investigated. Given the short time available for larval development, it is important that mating takes place as early as possible. The genetic data and earlier capture-recapture data suggest that R. arvalis gather at mating grounds they are familiar with. However, by forming leks in random to relatedness, and having multiple paternities in single clutches, the risk of inbreeding may be minimized in this otherwise highly philopatric species.

Population dynamics of blue mussels in a variable environment at the edge of their range

Spatial and temporal variation in the abundance of species can often be ascribed to spatial and temporal variation in the surrounding environment. Knowledge of how biotic and abiotic factors operate over different spatial and temporal scales in determining distribution, abundance, and structure of populations lies at the heart of ecology. The major part of the current ecological theory stems from studies carried out in central parts of the distributional range of species, whereas knowledge of how marginal populations function is inadequate. Understanding how marginal populations, living at the edge of their range, function is however in a key position to advance ecology and evolutionary biology as scientific disciplines. My thesis focuses on the factors affecting dynamics of marginal populations of blue mussels (Mytilus edulis) living close to their tolerance limits with regard to salinity. The thesis aims to highlight the dynamics at the edge of the range and contrast these with dynamics in more central parts of the range in order to understand the potential interplay between the central and the marginal part in the focal system. The objectives of the thesis are approached by studies on: (1) factors affecting regional patterns of the species, (2) long-term temporal dynamics of the focal species spaced along a regional salinity gradient, (3) selective predation by increasing populations of roach (Rutilus rutilus) when feeding on their main food item, the blue mussel, (4) the primary and secondary effects of local wave exposure gradients and (5) the role of small-scale habitat heterogeneity as determinants of large-scale pattern. The thesis shows that populations of blue mussels are largely determined by large scale changes in sea water salinity, affecting mainly recruitment success and longevity of local populations. In opposite to the traditional view, the thesis strongly indicate that vertebrate predators strongly affect abundance and size structure of blue mussel populations, and that the role of these predators increases towards the margin where populations are increasingly top-down controlled. The thesis also indicates that the positive role of biogenic habitat modifiers increases towards the marginal areas, where populations of blue mussels are largely recruitment limited. Finally, the thesis shows that local blue mussel populations are strongly dependent on high water turbulence, and therefore, dense populations are constrained to offshore habitats. Finally, the thesis suggests that ongoing sedimentation of rocky shores is detrimental for the species, affecting recruitment success and post-recruit survival, pushing stable mussel beds towards offshore areas. Ongoing large scale changes in the Baltic Sea, especially dilution processes with attendant effects, are predicted to substantially contract the distributional range of the mussel, but also affect more central populations. The thesis shows that in order to understand the functioning of marginal populations, research should (1) strive for multi-scale approaches in order to link ecosystem patterns with ecosystem processes, and (2) challenge the prevailing tenets that origin from research carried out in central areas that may not be valid at the edge.

Human genetic variation in the Baltic Sea region: Features of population history and natural selection

In this thesis, the genetic variation of human populations from the Baltic Sea region was studied in order to elucidate population history as well as evolutionary adaptation in this region. The study provided novel understanding of how the complex population level processes of migration, genetic drift, and natural selection have shaped genetic variation in North European populations. Results from genome-wide, mitochondrial DNA and Y-chromosomal analyses suggested that the genetic background of the populations of the Baltic Sea region lies predominantly in Continental Europe, which is consistent with earlier studies and archaeological evidence. The late settlement of Fennoscandia after the Ice Age and the subsequent small population size have led to pronounced genetic drift, especially in Finland and Karelia but also in Sweden, evident especially in genome-wide and Y-chromosomal analyses. Consequently, these populations show striking genetic differentiation, as opposed to much more homogeneous pattern of variation in Central European populations. Additionally, the eastern side of the Baltic Sea was observed to have experienced eastern influence in the genome-wide data as well as in mitochondrial DNA and Y-chromosomal variation – consistent with linguistic connections. However, Slavic influence in the Baltic Sea populations appears minor on genetic level. While the genetic diversity of the Finnish population overall was low, genome-wide and Y-chromosomal results showed pronounced regional differences. The genetic distance between Western and Eastern Finland was larger than for many geographically distant population pairs, and provinces also showed genetic differences. This is probably mainly due to the late settlement of Eastern Finland and local isolation, although differences in ancestral migration waves may contribute to this, too. In contrast, mitochondrial DNA and Y-chromosomal analyses of the contemporary Swedish population revealed a much less pronounced population structure and a fusion of the traces of ancient admixture, genetic drift, and recent immigration. Genome-wide datasets also provide a resource for studying the adaptive evolution of human populations. This study revealed tens of loci with strong signs of recent positive selection in Northern Europe. These results provide interesting targets for future research on evolutionary adaptation, and may be important for understanding the background of disease-causing variants in human populations.

From actin monomers to bundles: The roles of twinfilin and α-actinin in Drosophila melanogaster development

The actin cytoskeleton is essential for a large variety of cell biological processes. Actin exists in either a monomeric or a filamentous form, and it is very important for many cellular functions that the local balance between these two actin populations is properly regulated. A large number of proteins participate in the regulation of actin dynamics in the cell, and twinfilin, one of the proteins examined in this thesis, belongs to this category. The second level of regulation involves proteins that crosslink or bundle actin filaments, thereby providing the cell with a certain shape. α-Actinin, the second protein studied, mainly acts as an actin crosslinking protein. Both proteins are conserved in organisms ranging from yeast to mammals. In this thesis, the roles of twinfilin and α-actinin in development were examined using Drosophila melanogaster as a model organism. Twinfilin is an actin monomer binding protein that is structurally related to cofilin. In vitro, twinfilin reduces actin polymerisation by sequestering actin monomers. The Drosophila twinfilin (twf) gene was identified and found to encode a protein functionally similar to yeast and mammalian twinfilins. A strong hypomorphic twf mutation was identified, and flies homozygous for this allele were viable and fertile. The adult twf mutant flies displayed reduced viability, a rough eye phenotype and severely malformed bristles. The shape of the adult bristle is determined by the actin bundles that are regularly spaced around the perimeter of the developing pupal bristles. Examination of the twf pupal bristles revealed an increased level of filamentous actin, which in turn resulted in splitting and displacement of the actin bundles. The bristle defect was rescued by twf overexpression in developing bristles. The Twinfilin protein was localised at sites of actin filament assembly, where it was required to limit actin polymerisation. A genetic interaction between twinfilin and twinstar (the gene encoding Cofilin) was detected, consistent with the model predicting that both proteins act to limit the amount of filamentous actin. α-Actinin has been implicated in several diverse cell biological processes. In Drosophila, the only function for α-actinin yet known is in the organisation of the muscle sarcomere. Muscle and non-muscle cells utilise different α-actinin isoforms, which in Drosophila are produced by alternative splicing of a single gene. In this work, novel α-actinin deletion alleles, including ActnΔ233, were generated, which specifically disrupted the transcript encoding the non-muscle α-actinin isoform. Nevertheless, ActnΔ233 homozygous mutant flies were viable and fertile with no obvious defects. By comparing α-actinin protein distribution in wild type and ActnΔ233 mutant animals, it could be concluded that non-muscle α-actinin is the only isoform expressed in young embryos, in the embryonic central nervous system and in various actin-rich structures of the ovarian germline cells. In the ActnΔ233 mutant, α-actinin was detected not only in muscle tissue, but also in embryonic epidermal cells and in certain follicle cell populations in the ovaries. The population of α-actinin protein present in non-muscle cells of the ActnΔ233 mutant is referred to as FC-α-actinin (Follicle Cell). The follicular epithelium in the Drosophila ovary is a well characterised model system for studies on patterning and morphogenesis. Therefore, α-actinin expression, regulation and function in this tissue were further analysed. Examination of the α-actinin localisation pattern revealed that the basal actin fibres of the main body follicle cells underwent an organised remodelling during the final stages of oogenesis. This involved the assembly of a transient adhesion site in the posterior of the cell, in which α-actinin and Enabled (Ena) accumulated. Follicle cells genetically manipulated to lack all α-actinin isoforms failed to remodel their cytoskeleton and translocate Ena to the posterior of the cell, while the actin fibres as such were not affected. Neither was epithelial morphogenesis disrupted. The reorganisation of the basal actin cytoskeleton was also disturbed following ectopic expression of Decapentaplegic (Dpp) or as a result of a heat shock. At late oogenesis, the main body follicle cells express both non-muscle α-actinin and FC-α-actinin, while the dorsal anterior follicle cells express only non-muscle α-actinin. The dorsal anterior cells are patterned by the Dpp and Epidermal growth factor receptor (EGFR) signalling pathways, and they will ultimately secrete the dorsal appendages of the egg. Experiments involving ectopic activation of EGFR and Dpp signalling showed that FC-α-actinin is negatively regulated by combined EGFR and Dpp signalling. Ubiquitous overexpression of the adult muscle-specific α-actinin isoform induced the formation of aberrant actin bundles in migrating follicle cells that did not normally express FC-α-actinin, provided that the EGFR signalling pathway was activated in the cells. Taken together, this work contributes new data to our knowledge of α-actinin function and regulation in Drosophila. The cytoskeletal remodelling shown to depend on α-actinin function provides the first evidence that α-actinin has a role in the organisation of the cytoskeleton in a non-muscle tissue. Furthermore, the cytoskeletal remodelling constitutes a previously undescribed morphogenetic event, which may provide us with a model system for in vivo studies on adhesion dynamics in Drosophila.

Applications of coralline hydroxyapatite with bioabsorbable containment and reinforcement as bone graft substitute : An experimental study

The aim of the present experimental study was to find out if the applications of coralline hydroxyapatite (HA) can be improved by using bioabsorbable containment or binding substance with particulate HA in mandibular contour augmentation and by using bioabsorbable fibre-reinforced HA blocks in filling bone defects and in anterior lumbar interbody fusion. The use of a separate curved polyglycolide (PGA) containment alone or together with a fast resorbing polyglycolide/polylactide (PGA/PLA) binding substance were compared to the conventional non-contained method in ridge augmentation in sheep. The contained methods decreased HA migration, but the augmentations did not differ significantly. The use of the containment caused a risk for wound dehiscence and infection. Histologically there was a rapid connective tissue ingrowth into the HA graft and it was more abundant with the PGA containment compared to the non-contained augmentation and even additionally rich when the HA particles were bound with PGA/PLA copolymer. However, the bone ingrowth was best in the non-contained augmentation exceeding 10-12 % of the total graft area at 24 weeks. Negligible or no bone ingrowth was seen in the cases where the polymer composite was added to the HA particles and, related to that, foreign-body type cells were seen at the interface between the HA and host bone. The PGA and poly-dl/l-lactide (PDLLA) fibre-reinforced coralline HA blocks were studied in the metaphyseal and in the diaphyseal defects in rabbits. A rapid bone ingrowth was seen inside the both types of implants. Both PGA and PDLLA fibres induced an inflammatory fibrous reaction around themselves but it did not hinder the bone ingrowth. The bone ingrowth pattern was directed according to the loading conditions so that the load-carrying cortical ends of the implants as well as the implants sited in the diaphyseal defects were the most ossified. The fibre-reinforced coralline HA implants were further studied as stand-alone grafts in the lumbar anterior interbody implantation in pigs. The strength of the HA implants proved not to be adequate, the implants fractured in six weeks and the disc space was gradually lost similarly to that of the discectomized spaces. Histologically, small quantities of bone ingrowth was seen in some of the PGA and PDLLA reinforced coralline implants while no bone formation was identified in any of the PDLLA reinforced synthetic porous HA implants. While fragmented, the inner structure of the implants was lost, the bone ingrowth was minimal, and the disc was replaced by the fibrous connective tissue. When evaluated radiologically the grade of ossification was assessed as better than histologically, and, when related to the histologic findings, CT was more dependable than the plain films to show ossification of the implanted disc space. Local kyphosis was a frequent finding along with anterior bone bridging and ligament ossification as a consequence of instability of the implanted segment.