On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Mu in vitro transposition applications in protein engineering

Transposons, mobile genetic elements that are ubiquitous in all living organisms have been used as tools in molecular biology for decades. They have the ability to move into discrete DNA locations with no apparent homology to the target site. The utility of transposons as molecular tools is based on their ability to integrate into various DNA sequences efficiently, producing extensive mutant clone libraries that can be used in various molecular biology applications. Bacteriophage Mu is one of the most useful transposons due to its well-characterized and simple in vitro transposition reaction. This study establishes the properties of the Mu in vitro transposition system as a versatile multipurpose tool in molecular biology. In addition, this study describes Mu-based applications for engineering proteins by random insertional transposon mutagenesis in order to study structure-function relationships in proteins. We initially characterized the properties of the minimal Mu in vitro transposition system. We showed that the Mu transposition system works efficiently and accurately and produces insertions into a wide spectrum of target sites in different DNA molecules. Then, we developed a pentapeptide insertion mutagenesis strategy for inserting random five amino acid cassettes into proteins. These protein variants can be used especially for screening important sites for protein-protein interactions. Also, the system may produce temperature-sensitive variants of the protein of interest. Furthermore, we developed an efficient screening system for high-resolution mapping of protein-protein interfaces with the pentapeptide insertion mutagenesis. This was accomplished by combining the mutagenesis with subsequent yeast two-hybrid screening and PCR-based genetic footprinting. This combination allows the analysis of the whole mutant library en masse, without the need for producing or isolating separate mutant clones, and the protein-protein interfaces can be determined at amino acid accuracy. The system was validated by analysing the interacting region of JFC1 with Rab8A, and we show that the interaction is mediated via the JFC1 Slp homology domain. In addition, we developed a procedure for the production of nested sets of N- and C-terminal deletion variants of proteins with the Mu system. These variants are useful in many functional studies of proteins, especially in mapping regions involved in protein-protein interactions. This methodology was validated by analysing the region in yeast Mso1 involved in an interaction with Sec1. The results of this study show that the Mu in vitro transposition system is versatile for various applicational purposes and can efficiently be adapted to random protein engineering applications for functional studies of proteins.

Barrett's Esophagus and Associated Adenocarcinoma : studies on pathogenesis, clinical staging and cost-utility of cancer treatment

Esophageal and gastroesophageal junction (GEJ) adenocarcinoma is rapidly increasing disease with a pathophysiology connected to oxidative stress. Exact pre-treatment clinical staging is essential for optimal care of this lethal malignancy. The cost-effectiviness of treatment is increasingly important. We measured oxidative metabolism in the distal and proximal esophagus by myeloperoxidase activity (MPA), glutathione content (GSH), and superoxide dismutase (SOD) in 20 patients operated on with Nissen fundoplication and 9 controls during a 4-year follow-up. Further, we assessed the oxidative damage of DNA by 8-hydroxydeoxyguanosine (8-OHdG) in esophageal samples of subjects (13 Barrett s metaplasia, 6 Barrett s esophagus with high-grade dysplasia, 18 adenocarcinoma of the distal esophagus/GEJ, and 14 normal controls). We estimated the accuracy (42 patients) and preoperative prognostic value (55 patients) of PET compared with computed tomography (CT) and endoscopic ultrasound (EUS) in patients with adenocarcinoma of the esophagus/GEJ. Finally, we clarified the specialty-related costs and the utility of either radical (30 patients) or palliative (23 patients) treatment of esophageal/GEJ carcinoma by the 15 D health-related quality-of-life (HRQoL) questionnaire and the survival rate. The cost-utility of radical treatment of esophageal/GEJ carcinoma was investigated using a decision tree analysis model comparing radical, palliative, and hypothetical new treatment. We found elevated oxidative stress ( measured by MPA) and decreased antioxidant defense (measured by GSH) after antireflux surgery. This indicates that antireflux surgery is not a perfect solution for oxidative stress of the esophageal mucosa. Elevated oxidative stress in turn may partly explain why adenocarcinoma of the distal esophagus is found even after successful fundoplication. In GERD patients, proximal esophageal mucosal anti-oxidative defense seems to be defective before and even years after successful antireflux surgery. In addition, antireflux surgery apparently does not change the level of oxidative stress in the proximal esophagus, suggesting that defective mucosal anti-oxidative capacity plays a role in development of oxidative damage to the esophageal mucosa in GERD. In the malignant transformation of Barrett s esophagus an important component appears to be oxidative stress. DNA damage may be mediated by 8-OHdG, which we found to be increased in Barrett s epithelium and in high-grade dysplasia as well as in adenocarcinoma of the esophagus/GEJ compared with controls. The entire esophagus of Barrett s patients suffers from increased oxidative stress ( measured by 8-OhdG). PET is a useful tool in the staging and prognostication of adenocarcinoma of the esophagus/GEJ detecting organ metastases better than CT, although its accuracy in staging of paratumoral and distant lymph nodes is limited. Radical surgery for esophageal/GEJ carcinoma provides the greatest benefit in terms of survival, and its cost-utility appears to be the best of currently available treatments.

Rolling tachyons, random matrices, and Coulomb gas thermodynamics

Time-dependent backgrounds in string theory provide a natural testing ground for physics concerning dynamical phenomena which cannot be reliably addressed in usual quantum field theories and cosmology. A good, tractable example to study is the rolling tachyon background, which describes the decay of an unstable brane in bosonic and supersymmetric Type II string theories. In this thesis I use boundary conformal field theory along with random matrix theory and Coulomb gas thermodynamics techniques to study open and closed string scattering amplitudes off the decaying brane. The calculation of the simplest example, the tree-level amplitude of n open strings, would give us the emission rate of the open strings. However, even this has been unknown. I will organize the open string scattering computations in a more coherent manner and will argue how to make further progress.

Markov random fields and spatial smoothing in improving of forest inventory estimates

Markov random fields (MRF) are popular in image processing applications to describe spatial dependencies between image units. Here, we take a look at the theory and the models of MRFs with an application to improve forest inventory estimates. Typically, autocorrelation between study units is a nuisance in statistical inference, but we take an advantage of the dependencies to smooth noisy measurements by borrowing information from the neighbouring units. We build a stochastic spatial model, which we estimate with a Markov chain Monte Carlo simulation method. The smooth values are validated against another data set increasing our confidence that the estimates are more accurate than the originals.

Aspiration-based utility functions in a planning model for timber flow management.

The study presents a theory of utility models based on aspiration levels, as well as the application of this theory to the planning of timber flow economics. The first part of the study comprises a derivation of the utility-theoretic basis for the application of aspiration levels. Two basic models are dealt with: the additive and the multiplicative. Applied here solely for partial utility functions, aspiration and reservation levels are interpreted as defining piecewisely linear functions. The standpoint of the choices of the decision-maker is emphasized by the use of indifference curves. The second part of the study introduces a model for the management of timber flows. The model is based on the assumption that the decision-maker is willing to specify a shape of income flow which is different from that of the capital-theoretic optimum. The utility model comprises four aspiration-based compound utility functions. The theory and the flow model are tested numerically by computations covering three forest holdings. The results show that the additive model is sensitive even to slight changes in relative importances and aspiration levels. This applies particularly to nearly linear production possibility boundaries of monetary variables. The multiplicative model, on the other hand, is stable because it generates strictly convex indifference curves. Due to a higher marginal rate of substitution, the multiplicative model implies a stronger dependence on forest management than the additive function. For income trajectory optimization, a method utilizing an income trajectory index is more efficient than one based on the use of aspiration levels per management period. Smooth trajectories can be attained by squaring the deviations of the feasible trajectories from the desired one.

Light scattering in random media with wavelength-scale structures : astronomical and industrial applications

Light scattering, or scattering and absorption of electromagnetic waves, is an important tool in all remote-sensing observations. In astronomy, the light scattered or absorbed by a distant object can be the only source of information. In Solar-system studies, the light-scattering methods are employed when interpreting observations of atmosphereless bodies such as asteroids, atmospheres of planets, and cometary or interplanetary dust. Our Earth is constantly monitored from artificial satellites at different wavelengths. With remote sensing of Earth the light-scattering methods are not the only source of information: there is always the possibility to make in situ measurements. The satellite-based remote sensing is, however, superior in the sense of speed and coverage if only the scattered signal can be reliably interpreted. The optical properties of many industrial products play a key role in their quality. Especially for products such as paint and paper, the ability to obscure the background and to reflect light is of utmost importance. High-grade papers are evaluated based on their brightness, opacity, color, and gloss. In product development, there is a need for computer-based simulation methods that could predict the optical properties and, therefore, could be used in optimizing the quality while reducing the material costs. With paper, for instance, pilot experiments with an actual paper machine can be very time- and resource-consuming. The light-scattering methods presented in this thesis solve rigorously the interaction of light and material with wavelength-scale structures. These methods are computationally demanding, thus the speed and accuracy of the methods play a key role. Different implementations of the discrete-dipole approximation are compared in the thesis and the results provide practical guidelines in choosing a suitable code. In addition, a novel method is presented for the numerical computations of orientation-averaged light-scattering properties of a particle, and the method is compared against existing techniques. Simulation of light scattering for various targets and the possible problems arising from the finite size of the model target are discussed in the thesis. Scattering by single particles and small clusters is considered, as well as scattering in particulate media, and scattering in continuous media with porosity or surface roughness. Various techniques for modeling the scattering media are presented and the results are applied to optimizing the structure of paper. However, the same methods can be applied in light-scattering studies of Solar-system regoliths or cometary dust, or in any remote-sensing problem involving light scattering in random media with wavelength-scale structures.