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.

Dancing and Professional Dancers in Roman Egypt

The main aim of the study is to create a many-sided view of dancing in Roman Egypt (1st - early 4th centuries AD) and especially of the dancers who earned their living by dancing as hired performers. Even though dancers and other performers played a central part in many kinds of festivities throughout the ancient world, research on ancient professional dancers is rare and tends to rest on the ancient literature, which reflects the opinions of the elite. Documentary written sources (i.e., papyri, ostraka) the core of the present study are mentioned rather superficially, easily resulting in a stereotypical view of the dancers. This study will balance the picture of professional dancers in antiquity and of ancient dancing in a more general sense. The second aim characterizes this study as basic research: to provide a corpus of written sources from Greco-Roman Egypt on dancing and to discuss pictorial sources contemporary with the texts. The study also takes into account the theoretical discussion that centres on dancing as a nonverbal communicative mode. Dancers are seen as significant conveyors of social and cultural matters. This study shows that dancers were hired to perform especially in religious contexts, where the local associations on the village level also played an important part as the employers of the performers. These performers had a better standard of living in economic terms than the average hired worker, and dancers were better paid than other performers. In the Egyptian villages and towns, where the dancers performed and lived, the dancers do not seem to have been marginal because they were professionals or because of some ethnic or social background. However, their possible marginality may have occurred for reasons related to the practicalities of their profession (e.g., the itinerant life style). The oriental background of performers was a literary topos reflecting partly the situation in the centres of the empire, especially Rome, where many performers were of other than Roman origin. The connection of dancing, prostitution and slavery reflects the essential link between dance, body and gender: dancers are equated with such professions or socio-legal statuses where the body is the focus of attention, a commodity and a source of sensual pleasure; this dimension is clearly observable in ancient literature. According to the Egyptian documentary sources, there is no watertight evidence that professional dancers would have been engaged in prostitution and very little, if any, evidence that the disapproval of the professional dancers expressed by the ancient authors was shared by the Egyptians. From the 4th century onwards the dancers almost disappear from the documentary sources, reflecting the political and religious changes in the Mediterranean east.

Sijaissotilasjärjestelmä ja väenotot : Taloudellis-sosiaalinen tutkimus sijaissotilaiden käytöstä Ala-Satakunnan väenotoissa vuosina 1631-1648

The dissertation describes the conscription of Finnish soldiers into the Swedish army during the Thirty Years' War. The work concentrates on so-called substitute soldiers, who were hired for conscription by wealthier peasants, who thus avoided the draft. The substitutes were the largest group recruited by the Swedish army in Sweden. The substitutes made up approximately 25-80% of the total number of soldiers. They recieved a significant sum of money from the peasants: about 50-250 Swedish copper dalers, corresponding to the price of a little peasant house. The practice of using substitutes was managed by the local village council. The recruits were normally from the landless population. However, when there was an urgent need of men, even the yeoman had to leave their homes for the distant garrisons across the Baltic. Conscription and its devastating effect on agricultural production also reduced the flow of state revenues. One of the tasks of the dissertation is the correlation between the custom of using substitutes and the abandonment of farmsteds (= in to the first place, to the non-ability to pay taxes). In areas where there were no substitutes available the peasants had to join the army themselves, which normally led to abandonment and financial ruin because agricultural production was based on physical labour. This led to rise of large farms at the cost of smaller ones. Hence, the system of substitutes was a factor that transformed the mode of settlement.

The efficacy and potential risks of controlling sprouting in Finnish birches (Betula spp.) with the fungal decomposer Chondrostereum purpureum

Sprouting of fast-growing broad-leaved trees causes problems in young coniferous stands, under power transmission lines and along roads and railways. Public opinion and the Finnish Forest Certification System oppose the use of chemical herbicides to control sprouting, which means that most areas with problems rely on mechanical cutting. However, cutting is a poor control method for many broad-leaved species because the removal of leaders can stimulate the sprouting of side branches and cut stumps quickly re-sprout. In order to be effective, cutting must be carried out frequently but each cut increases the costs, making this control method increasingly difficult and expensive once begun. As such, alternative methods for sprout control that are both effective and environmentally sound represent a continuing challenge to managers and research biologists. Using biological control agents to prevent sprouting has been given serious consideration recently. Dutch and Canadian researchers have demonstrated the potential of the white-rot fungus Chondrostereum purpureum (Pers. ex Fr.) Pouzar as a control agent of stump sprouting in many hardwoods. These findings have focused the attention of the Finnish forestry community on the utilization of C. purpureum for biocontrol purposes. Primarily, this study sought determines the efficacy of native C. purpureum as an inhibitor of birch stump sprouting in Finland and to clarify its mode of action. Additionally, genotypic variation in Finnish C. purpureum was examined and the environmental risks posed by a biocontrol program using this fungus were assessed. Experimental results of the study demonstrated that C. purpureum clearly affects the sprouting of birch: both the frequency of living stumps and the number of living sprouts per stump were effectively reduced by the treatment. However, the treatment had no effect on the maximum height of new sprouts. There were clear differences among fungal isolates in preventing sprouting and those that possessed high oxidative activities as measured in the laboratory inhibited sprouting most efficiently in the field. The most effective treatment time during the growing season was in early and mid summer (May July). Genetic diversity in Nordic and Baltic populations of C. purpureum was found to be high at the regional scale but locally homogeneous. This natural distribution of diversity means that using local genotypes in biocontrol programs would effectively prevent the introduction of novel genes or genotypes. While a biocontrol program using local strains of C. purpureum would be environmentally neutral, pruned birches that are close to the treatment site would have a high susceptibility to infect by the fungus during the early spring.

Estimation of local forest attributes, utilizing two-phase sampling and auxiliary data

This thesis examines the feasibility of a forest inventory method based on two-phase sampling in estimating forest attributes at the stand or substand levels for forest management purposes. The method is based on multi-source forest inventory combining auxiliary data consisting of remote sensing imagery or other geographic information and field measurements. Auxiliary data are utilized as first-phase data for covering all inventory units. Various methods were examined for improving the accuracy of the forest estimates. Pre-processing of auxiliary data in the form of correcting the spectral properties of aerial imagery was examined (I), as was the selection of aerial image features for estimating forest attributes (II). Various spatial units were compared for extracting image features in a remote sensing aided forest inventory utilizing very high resolution imagery (III). A number of data sources were combined and different weighting procedures were tested in estimating forest attributes (IV, V). Correction of the spectral properties of aerial images proved to be a straightforward and advantageous method for improving the correlation between the image features and the measured forest attributes. Testing different image features that can be extracted from aerial photographs (and other very high resolution images) showed that the images contain a wealth of relevant information that can be extracted only by utilizing the spatial organization of the image pixel values. Furthermore, careful selection of image features for the inventory task generally gives better results than inputting all extractable features to the estimation procedure. When the spatial units for extracting very high resolution image features were examined, an approach based on image segmentation generally showed advantages compared with a traditional sample plot-based approach. Combining several data sources resulted in more accurate estimates than any of the individual data sources alone. The best combined estimate can be derived by weighting the estimates produced by the individual data sources by the inverse values of their mean square errors. Despite the fact that the plot-level estimation accuracy in two-phase sampling inventory can be improved in many ways, the accuracy of forest estimates based mainly on single-view satellite and aerial imagery is a relatively poor basis for making stand-level management decisions.

Plant species diversity of buffer zones in agricultural landscapes: in search of determinants from the local to regional scale

Buffer zones are vegetated strip-edges of agricultural fields along watercourses. As linear habitats in agricultural ecosystems, buffer strips dominate and play a leading ecological role in many areas. This thesis focuses on the plant species diversity of the buffer zones in a Finnish agricultural landscape. The main objective of the present study is to identify the determinants of floral species diversity in arable buffer zones from local to regional levels. This study was conducted in a watershed area of a farmland landscape of southern Finland. The study area, Lepsämänjoki, is situated in the Nurmijärvi commune 30 km to the north of Helsinki, Finland. The biotope mosaics were mapped in GIS. A total of 59 buffer zones were surveyed, of which 29 buffer strips surveyed were also sampled by plot. Firstly, two diversity components (species richness and evenness) were investigated to determine whether the relationship between the two is equal and predictable. I found no correlation between species richness and evenness. The relationship between richness and evenness is unpredictable in a small-scale human-shaped ecosystem. Ordination and correlation analyses show that richness and evenness may result from different ecological processes, and thus should be considered separately. Species richness correlated negatively with phosphorus content, and species evenness correlated negatively with the ratio of organic carbon to total nitrogen in soil. The lack of a consistent pattern in the relationship between these two components may be due to site-specific variation in resource utilization by plant species. Within-habitat configuration (width, length, and area) were investigated to determine which is more effective for predicting species richness. More species per unit area increment could be obtained from widening the buffer strip than from lengthening it. The width of the strips is an effective determinant of plant species richness. The increase in species diversity with an increase in the width of buffer strips may be due to cross-sectional habitat gradients within the linear patches. This result can serve as a reference for policy makers, and has application value in agricultural management. In the framework of metacommunity theory, I found that both mass effect(connectivity) and species sorting (resource heterogeneity) were likely to explain species composition and diversity on a local and regional scale. The local and regional processes were interactively dominated by the degree to which dispersal perturbs local communities. In the lowly and intermediately connected regions, species sorting was of primary importance to explain species diversity, while the mass effect surpassed species sorting in the highly connected region. Increasing connectivity in communities containing high habitat heterogeneity can lead to the homogenization of local communities, and consequently, to lower regional diversity, while local species richness was unrelated to the habitat connectivity. Of all species found, Anthriscus sylvestris, Phalaris arundinacea, and Phleum pretense significantly responded to connectivity, and showed high abundance in the highly connected region. We suggest that these species may play a role in switching the force from local resources to regional connectivity shaping the community structure. On the landscape context level, the different responses of local species richness and evenness to landscape context were investigated. Seven landscape structural parameters served to indicate landscape context on five scales. On all scales but the smallest scales, the Shannon-Wiener diversity of land covers (H') correlated positively with the local richness. The factor (H') showed the highest correlation coefficients in species richness on the second largest scale. The edge density of arable field was the only predictor that correlated with species evenness on all scales, which showed the highest predictive power on the second smallest scale. The different predictive power of the factors on different scales showed a scaledependent relationship between the landscape context and local plant species diversity, and indicated that different ecological processes determine species richness and evenness. The local richness of species depends on a regional process on large scales, which may relate to the regional species pool, while species evenness depends on a fine- or coarse-grained farming system, which may relate to the patch quality of the habitats of field edges near the buffer strips. My results suggested some guidelines of species diversity conservation in the agricultural ecosystem. To maintain a high level of species diversity in the strips, a high level of phosphorus in strip soil should be avoided. Widening the strips is the most effective mean to improve species richness. Habitat connectivity is not always favorable to species diversity because increasing connectivity in communities containing high habitat heterogeneity can lead to the homogenization of local communities (beta diversity) and, consequently, to lower regional diversity. Overall, a synthesis of local and regional factors emerged as the model that best explain variations in plant species diversity. The studies also suggest that the effects of determinants on species diversity have a complex relationship with scale.

The Significance of Wild Plants in the Evolutionary Ecology of Three Major Viruses Infecting Cultivated Sweetpotato in Uganda

The studies presented in this thesis contribute to the understanding of evolutionary ecology of three major viruses threatening cultivated sweetpotato (Ipomoea batatas Lam) in East Africa: Sweet potato feathery mottle virus (SPFMV; genus Potyvirus; Potyviridae), Sweet potato chlorotic stunt virus (SPCSV; genus Crinivirus; Closteroviridae) and Sweet potato mild mottle virus (SPMMV; genus Ipomovirus; Potyviridae). The viruses were serologically detected and the positive results confirmed by RT-PCR and sequencing. SPFMV was detected in 24 wild plant species of family Convolvulacea (genera Ipomoea, Lepistemon and Hewittia), of which 19 species were new natural hosts for SPFMV. SPMMV and SPCSV were detected in wild plants belonging to 21 and 12 species (genera Ipomoea, Lepistemon and Hewittia), respectively, all of which were previously unknown to be natural hosts of these viruses. SPFMV was the most abundant virus being detected in 17% of the plants, while SPMMV and SPCSV were detected in 9.8% and 5.4% of the assessed plants, respectively. Wild plants in Uganda were infected with the East African (EA), common (C), and the ordinary (O) strains, or co-infected with the EA and the C strain of SPFMV. The viruses and virus-like diseases were more frequent in the eastern agro-ecological zone than the western and central zones, which contrasted with known incidences of these viruses in sweetpotato crops, except for northern zone where incidences were lowest in wild plants as in sweetpotato. The NIb/CP junction in SPMMV was determined experimentally which facilitated CP-based phylogenetic and evolutionary analyses of SPMMV. Isolates of all the three viruses from wild plants were genetically similar to those found in cultivated sweetpotatoes in East Africa. There was no evidence of host-driven population genetic structures suggesting frequent transmission of these viruses between their wild and cultivated hosts. The p22 RNA silencing suppressor-encoding sequence was absent in a few SPCSV isolates, but regardless of this, SPCSV isolates incited sweet potato virus disease (SPVD) in sweetpotato plants co-infected with SPFMV, indicating that p22 is redundant for synergism between SCSV and SPFMV. Molecular evolutionary analysis revealed that isolates of strain EA of SPFMV that is largely restricted geographically in East Africa experience frequent recombination in comparison to isolates of strain C that is globally distributed. Moreover, non-homologous recombination events between strains EA and C were rare, despite frequent co-infections of these strains in wild plants, suggesting purifying selection against non-homologous recombinants between these strains or that such recombinants are mostly not infectious. Recombination was detected also in the 5 - and 3 -proximal regions of the SPMMV genome providing the first evidence of recombination in genus Ipomovirus, but no recombination events were detected in the characterized genomic regions of SPCSV. Strong purifying selection was implicated on evolution of majority of amino acids of the proteins encoded by the analyzed genomic regions of SPFMV, SPMMV and SPCSV. However, positive selection was predicted on 17 amino acids distributed over the whole the coat protein (CP) in the globally distributed strain C, as compared to only 4 amino acids in the multifunctional CP N-terminus (CP-NT) of strain EA largely restricted geographically to East Africa. A few amino acid sites in the N-terminus of SPMMV P1, the p7 protein and RNA silencing suppressor proteins p22 and RNase3 of SPCSV were also submitted to positive selection. Positively selected amino acids may constitute ligand-binding domains that determine interactions with plant host and/or insect vector factors. The P1 proteinase of SPMMV (genus Ipomovirus) seems to respond to needs of adaptation, which was not observed with the helper component proteinase (HC-Pro) of SPMMV, although the HC-Pro is responsible for many important molecular interactions in genus Potyvirus. Because the centre of origin of cultivated sweetpotato is in the Americas from where the crop was dispersed to other continents in recent history (except for the Australasia and South Pacific region), it would be expected that identical viruses and their strains occur worldwide, presuming virus dispersal with the host. Apparently, this seems not to be the case with SPMMV, the strain EA of SPFMV and the strain EA of SPCSV that are largely geographically confined in East Africa where they are predominant and occur both in natural and agro-ecosystems. The geographical distribution of plant viruses is constrained more by virus-vector relations than by virus-host interactions, which in accordance of the wide range of natural host species and the geographical confinement to East Africa suggest that these viruses existed in East African wild plants before the introduction of sweetpotato. Subsequently, these studies provide compelling evidence that East Africa constitutes a cradle of SPFMV strain EA, SPCSV strain EA, and SPMMV. Therefore, sweet potato virus disease (SPVD) in East Africa may be one of the examples of damaging virus diseases resulting from exchange of viruses between introduced crops and indigenous wild plant species. Keywords: Convolvulaceae, East Africa, epidemiology, evolution, genetic variability, Ipomoea, recombination, SPCSV, SPFMV, SPMMV, selection pressure, sweetpotato, wild plant species Author s Address: Arthur K. Tugume, Department of Agricultural Sciences, Faculty of Agriculture and Forestry, University of Helsinki, Latokartanonkaari 7, P.O Box 27, FIN-00014, Helsinki, Finland. Email: tugume.arthur@helsinki.fi Author s Present Address: Arthur K. Tugume, Department of Botany, Faculty of Science, Makerere University, P.O. Box 7062, Kampala, Uganda. Email: aktugume@botany.mak.ac.ug, tugumeka@yahoo.com

Molecular Modelling of Estrogen-Producing Enzymes CYP450 Aromatase and 17beta-Hydroxysteroid Dehydrogenase Type 1

Breast cancer is the most common cancer in women in the western countries. Approximately two-thirds of breast cancer tumours are hormone dependent, requiring estrogens to grow. Estrogens are formed in the human body via a multistep route starting from cholesterol. The final steps in the biosynthesis include the CYP450 aromatase enzyme, converting the male hormones androgens (preferred substrate androstenedione ASD) into estrogens(estrone E1), and the 17beta-HSD1 enzyme, converting the biologically less active E1 into the active hormone 17beta-hydroxyestradiol E2. E2 is bound to the nuclear estrogen receptors causing a cascade of biochemical reactions leading to cell proliferation in normal tissue, and to tumour growth in cancer tissue. Aromatase and 17beta-HSD1 are expressed in or near the breast tumour, locally providing the tissue with estrogens. One approach in treating hormone dependent breast tumours is to block the local estrogen production by inhibiting these two enzymes. Aromatase inhibitors are already on the market in treating breast cancer, despite the lack of an experimentally solved structure. The structure of 17beta-HSD1, on the other hand, has been solved, but no commercial drugs have emerged from the drug discovery projects reported in the literature. Computer-assisted molecular modelling is an invaluable tool in modern drug design projects. Modelling techniques can be used to generate a model of the target protein and to design novel inhibitors for them even if the target protein structure is unknown. Molecular modelling has applications in predicting the activities of theoretical inhibitors and in finding possible active inhibitors from a compound database. Inhibitor binding at atomic level can also be studied with molecular modelling. To clarify the interactions between the aromatase enzyme and its substrate and inhibitors, we generated a homology model based on a mammalian CYP450 enzyme, rabbit progesterone 21-hydroxylase CYP2C5. The model was carefully validated using molecular dynamics simulations (MDS) with and without the natural substrate ASD. Binding orientation of the inhibitors was based on the hypothesis that the inhibitors coordinate to the heme iron, and were studied using MDS. The inhibitors were dietary phytoestrogens, which have been shown to reduce the risk for breast cancer. To further validate the model, the interactions of a commercial breast cancer drug were studied with MDS and ligand–protein docking. In the case of 17beta-HSD1, a 3D QSAR model was generated on the basis of MDS of an enzyme complex with active inhibitor and ligand–protein docking, employing a compound library synthesised in our laboratory. Furthermore, four pharmacophore hypotheses with and without a bound substrate or an inhibitor were developed and used in screening a commercial database of drug-like compounds. The homology model of aromatase showed stable behaviour in MDS and was capable of explaining most of the results from mutagenesis studies. We were able to identify the active site residues contributing to the inhibitor binding, and explain differences in coordination geometry corresponding to the inhibitory activity. Interactions between the inhibitors and aromatase were in agreement with the mutagenesis studies reported for aromatase. Simulations of 17beta-HSD1 with inhibitors revealed an inhibitor binding mode with hydrogen bond interactions previously not reported, and a hydrophobic pocket capable of accommodating a bulky side chain. Pharmacophore hypothesis generation, followed by virtual screening, was able to identify several compounds that can be used in lead compound generation. The visualisation of the interaction fields from the QSAR model and the pharmacophores provided us with novel ideas for inhibitor development in our drug discovery project.

Spatial variation of climate and the impact of disturbances on local climate and forest recovery in northern Finland

The structure and function of northern ecosystems are strongly influenced by climate change and variability and by human-induced disturbances. The projected global change is likely to have a pronounced effect on the distribution and productivity of different species, generating large changes in the equilibrium at the tree-line. In turn, movement of the tree-line and the redistribution of species produce feedback to both the local and the regional climate. This research was initiated with the objective of examining the influence of natural conditions on the small-scale spatial variation of climate in Finnish Lapland, and to study the interaction and feedback mechanisms in the climate-disturbances-vegetation system near the climatological border of boreal forest. The high (1 km) resolution spatial variation of climate parameters over northern Finland was determined by applying the Kriging interpolation method that takes into account the effect of external forcing variables, i.e., geographical coordinates, elevation, sea and lake coverage. Of all the natural factors shaping the climate, the geographical position, local topography and altitude proved to be the determining ones. Spatial analyses of temperature- and precipitation-derived parameters based on a 30-year dataset (1971-2000) provide a detailed description of the local climate. Maps of the mean, maximum and minimum temperatures, the frost-free period and the growing season indicate that the most favourable thermal conditions exist in the south-western part of Lapland, around large water bodies and in the Kemijoki basin, while the coldest regions are in highland and fell Lapland. The distribution of precipitation is predominantly longitudinally dependent but with the definite influence of local features. The impact of human-induced disturbances, i.e., forest fires, on local climate and its implication for forest recovery near the northern timberline was evaluated in the Tuntsa area of eastern Lapland, damaged by a widespread forest fire in 1960 and suffering repeatedly-failed vegetation recovery since that. Direct measurements of the local climate and simulated heat and water fluxes indicated the development of a more severe climate and physical conditions on the fire-disturbed site. Removal of the original, predominantly Norway spruce and downy birch vegetation and its substitution by tundra vegetation has generated increased wind velocity and reduced snow accumulation, associated with a large variation in soil temperature and moisture and deep soil frost. The changed structural parameters of the canopy have determined changes in energy fluxes by reducing the latter over the tundra vegetation. The altered surface and soil conditions, as well as the evolved severe local climate, have negatively affected seedling growth and survival, leading to more unfavourable conditions for the reproduction of boreal vegetation and thereby causing deviations in the regional position of the timberline. However it should be noted that other factors, such as an inadequate seed source or seedbed, the poor quality of the soil and the intensive logging of damaged trees could also exacerbate the poor tree regeneration. In spite of the failed forest recovery at Tunsta, the position and composition of the timberline and tree-line in Finnish Lapland may also benefit from present and future changes in climate. The already-observed and the projected increase in temperature, the prolonged growing season, as well as changes in the precipitation regime foster tree growth and new regeneration, resulting in an advance of the timberline and tree-line northward and upward. This shift in the distribution of vegetation might be decelerated or even halted by local topoclimatic conditions and by the expected increase in the frequency of disturbances.

Individuals on the Move : Body Condition Dependent Dispersal and Quasi-Local Competition in Metapopulations

Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

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.