Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Multi-user resource-sharing problem for the Internet

In this thesis we study a series of multi-user resource-sharing problems for the Internet, which involve distribution of a common resource among participants of multi-user systems (servers or networks). We study concurrently accessible resources, which for end-users may be exclusively accessible or non-exclusively. For all kinds we suggest a separate algorithm or a modification of common reputation scheme. Every algorithm or method is studied from different perspectives: optimality of protocols, selfishness of end users, fairness of the protocol for end users. On the one hand the multifaceted analysis allows us to select the most suited protocols among a set of various available ones based on trade-offs of optima criteria. On the other hand, the future Internet predictions dictate new rules for the optimality we should take into account and new properties of the networks that cannot be neglected anymore. In this thesis we have studied new protocols for such resource-sharing problems as the backoff protocol, defense mechanisms against Denial-of-Service, fairness and confidentiality for users in overlay networks. For backoff protocol we present analysis of a general backoff scheme, where an optimization is applied to a general-view backoff function. It leads to an optimality condition for backoff protocols in both slot times and continuous time models. Additionally we present an extension for the backoff scheme in order to achieve fairness for the participants in an unfair environment, such as wireless signal strengths. Finally, for the backoff algorithm we suggest a reputation scheme that deals with misbehaving nodes. For the next problem -- denial-of-service attacks, we suggest two schemes that deal with the malicious behavior for two conditions: forged identities and unspoofed identities. For the first one we suggest a novel most-knocked-first-served algorithm, while for the latter we apply a reputation mechanism in order to restrict resource access for misbehaving nodes. Finally, we study the reputation scheme for the overlays and peer-to-peer networks, where resource is not placed on a common station, but spread across the network. The theoretical analysis suggests what behavior will be selected by the end station under such a reputation mechanism.

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.

Modeling Efficient Classification as a Process of Confidence Assessment and Delegation

In visual object detection and recognition, classifiers have two interesting characteristics: accuracy and speed. Accuracy depends on the complexity of the image features and classifier decision surfaces. Speed depends on the hardware and the computational effort required to use the features and decision surfaces. When attempts to increase accuracy lead to increases in complexity and effort, it is necessary to ask how much are we willing to pay for increased accuracy. For example, if increased computational effort implies quickly diminishing returns in accuracy, then those designing inexpensive surveillance applications cannot aim for maximum accuracy at any cost. It becomes necessary to find trade-offs between accuracy and effort. We study efficient classification of images depicting real-world objects and scenes. Classification is efficient when a classifier can be controlled so that the desired trade-off between accuracy and effort (speed) is achieved and unnecessary computations are avoided on a per input basis. A framework is proposed for understanding and modeling efficient classification of images. Classification is modeled as a tree-like process. In designing the framework, it is important to recognize what is essential and to avoid structures that are narrow in applicability. Earlier frameworks are lacking in this regard. The overall contribution is two-fold. First, the framework is presented, subjected to experiments, and shown to be satisfactory. Second, certain unconventional approaches are experimented with. This allows the separation of the essential from the conventional. To determine if the framework is satisfactory, three categories of questions are identified: trade-off optimization, classifier tree organization, and rules for delegation and confidence modeling. Questions and problems related to each category are addressed and empirical results are presented. For example, related to trade-off optimization, we address the problem of computational bottlenecks that limit the range of trade-offs. We also ask if accuracy versus effort trade-offs can be controlled after training. For another example, regarding classifier tree organization, we first consider the task of organizing a tree in a problem-specific manner. We then ask if problem-specific organization is necessary.

4QMMT - The Problem of the Epilogue

The main focus of this study is the epilogue of 4QMMT (4QMiqsat Ma aseh ha-Torah), a text of obscure genre containing a halakhic section found in cave 4 at Qumran. In the official edition published in the series Discoveries of the Judaean Desert (DJD X), the extant document was divided by its editors, Elisha Qimron and John Strugnell, into three literary divisions: Section A) the calendar section representing a 364-day solar calendar, Section B) the halakhot, and Section C) an epilogue. The work begins with text critical inspection of the manuscripts containing text from the epilogue (mss 4Q397, 4Q398, and 4Q399). However, since the relationship of the epilogue to the other sections of the whole document 4QMMT is under investigation, the calendrical fragments (4Q327 and 4Q394 3-7, lines 1-3) and the halakhic section also receive some attention, albeit more limited and purpose oriented. In Ch. 2, after a transcription of the fragments of the epilogue, a synopsis is presented in order to evaluate the composite text of the DJD X edition in light of the evidence provided by the individual manuscripts. As a result, several critical comments are offered, and finally, an alternative arrangement of the fragments of the epilogue with an English translation. In the following chapter (Ch. 3), the diversity of the two main literary divisions, the halakhic section and the epilogue, is discussed, and it is demonstrated that the author(s) of 4QMMT adopted and adjusted the covenantal pattern known from biblical law collections, more specifically Deuteronomy. The question of the genre of 4QMMT is investigated in Ch. 4. The final chapter (Ch. 5) contains an analysis of the use of Scripture in the epilogue. In a close reading, both the explicit citations and the more subtle allusions are investigated in an attempt to trace the theology of the epilogue. The main emphases of the epilogue are covenantal faithfulness, repentance and return. The contents of the document reflect a grave concern for the purity of the cult in Jerusalem, and in the epilogue Deuteronomic language and expressions are used to convince the readers of the necessity of a reformation. The large number of late copies found in cave 4 at Qumran witness the significance of 4QMMT and the continuous importance of the Jerusalem Temple for the Qumran community.

Sustainable forest management : ecologically sound and socially accepted

This dissertation explored the ecological dimension of ecologically sustainable forest management in boreal forests, and factors of the socio-cultural dimension that affect how the concept of ecologically sustainable forest management is defined. My approach was problem-oriented and generalistic-holistic. I examined associations between the abundances of wildlife groups (grouse, large predators, small predators, ungulates) and Siberian flying squirrels, and their co-occurrence with tree structural characteristics at the regional level. The trade-offs between ecological, social and economic sustainability in forestry were explored at the regional scale. I identified a potential 'shopping basket' of regional indicators for ecologically sustainable forest management, combining the relative abundance of Siberian flying squirrels, a wildlife richness index (WRI) for grouse, diversity indices of saw-timber trees, tree age classes and the proportion of old-growth (> 120 yr) forests. I suggest that the close association between forestry activity, the proportion of young forests (< 40 yr) and a WRI for small predators can be considered as potential 'alarm bells' for regions in which the creation of trade-offs (negative relationships) between economic and ecological components of sustainable forestry is ongoing. Explorative analyses revealed negative relationships between forestry activity and a WRI of 16 game species, the WRI for grouse and tree age diversity. Socially sustainable communities compete less intensively with ecological components of forests than communities where forestry is important. Interestingly, forest ownership types (farmers, other private forest owners, the forestry industry, the State) correlated significantly with the co-occurrence of flying squirrels, grouse and diverse forest structural characteristics rather than, for instance, with the total number of protection areas, suggesting that private forest ownership can lead to increased ecological sustainability. I examined forest actors’ argumentation to identify characteristics that affect the interpretation of ecologically sustainable forest management. Four argumentation frame types were constructed: information, work, experience and own position based. These differed in terms of their emphasis on external experts or own experiences. The closer ecologically sustainable forest management is to the forest actor’s daily life, the more profiled policy tools (counselling, learning through experiences) are needed to guide management behaviour to become more ecologically sound. I illustrated that forest actors interpret, use and understand information through meaningful framing. I analysed the extent to which ecological research information has been perceived in the Forestry Development Centre TAPIO’s recommendations and revised PEFC Finland criteria. We noticed that the political value for decaying wood was much lower in PEFC Finland critera (4 m3) than could be expected as a socially acceptable level (9 m3) or ecologically sound (10-20 m3). I consider it important for scientists to join political discourses and become involved in policy making concerning sustainable forest management to learn to present their results in a way that is reasonable from the user’s perspective.

Lignin biosynthesis in Norway spruce: from a model system to the tree

Lignin is a hydrophobic polymer that is synthesised in the secondary cell walls of all vascular plants. It enables water conduction through the stem, supports the upright growth habit and protects against invading pathogens. In addition, lignin hinders the utilisation of the cellulosic cell walls of plants in pulp and paper industry and as forage. Lignin precursors are synthesised in the cytoplasm through the phenylpropanoid pathway, transported into the cell wall and oxidised by peroxidases or laccases to phenoxy radicals that couple to form the lignin polymer. This study was conducted to characterise the lignin biosynthetic pathway in Norway spruce (Picea abies (L.) Karst.). We focused on the less well-known polymerisation stage, to identify the enzymes and the regulatory mechanisms that are involved. Available data for lignin biosynthesis in gymnosperms is scarce and, for example, the latest improvements in precursor biosynthesis have only been verified in herbaceous plants. Therefore, we also wanted to study in detail the roles of individual gene family members during developmental and stress-induced lignification, using EST sequencing and real-time RT-PCR. We used, as a model, a Norway spruce tissue culture line that produces extracellular lignin into the culture medium, and showed that lignin polymerisation in the tissue culture depends on peroxidase activity. We identified in the culture medium a significant NADH oxidase activity that could generate H2O2 for peroxidases. Two basic culture medium peroxidases were shown to have high affinity to coniferyl alcohol. Conservation of the putative substrate-binding amino acids was observed when the spruce peroxidase sequences were compared with other peroxidases with high affinity to coniferyl alcohol. We also used different peroxidase fractions to produce synthetic in vitro lignins from coniferyl alcohol; however, the linkage pattern of the suspension culture lignin could not be reproduced in vitro with the purified peroxidases, nor with the full complement of culture medium proteins. This emphasised the importance of the precursor radical concentration in the reaction zone, which is controlled by the cells through the secretion of both the lignin precursors and the oxidative enzymes to the apoplast. In addition, we identified basic peroxidases that were reversibly bound to the lignin precipitate. They could be involved, for example, in the oxidation of polymeric lignin, which is required for polymer growth. The dibenzodioxocin substructure was used as a marker for polymer oxidation in the in vitro polymerisation studies, as it is a typical substructure in wood lignin and in the suspension culture lignin. Using immunolocalisation, we found the structure mainly in the S2+S3 layers of the secondary cell walls of Norway spruce tracheids. The structure was primarily formed during the late phases of lignification. Contrary to the earlier assumptions, it appears to be a terminal structure in the lignin macromolecule. Most lignin biosynthetic enzymes are encoded for by several genes, all of which may not participate in lignin biosynthesis. In order to identify the gene family members that are responsible for developmental lignification, ESTs were sequenced from the lignin-forming tissue culture and developing xylem of spruce. Expression of the identified lignin biosynthetic genes was studied using real-time RT-PCR. Candidate genes for developmental lignification were identified by a coordinated, high expression of certain genes within the gene families in all lignin-forming tissues. However, such coordinated expression was not found for peroxidase genes. We also studied stress-induced lignification either during compression wood formation by bending the stems or after Heterobasidion annosum infection. Based on gene expression profiles, stress-induced monolignol biosynthesis appeared similar to the developmental process, and only single PAL and C3H genes were specifically up-regulated by stress. On the contrary, the up-regulated peroxidase genes differed between developmental and stress-induced lignification, indicating specific responses.

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.