Computing the diameter of Coxeter groups

This thesis addresses the problem of computing the minimal and maximal diameter of the Cayley graph of Coxeter groups. We first present and assert relevant parts of polytope theory and related Coxeter theory. After this, a method of contracting the orthogonal projections of a polytope from Rd onto R2 and R3, d ¸ 3 is presented. This method is the Equality Set Projection algorithm that requires a constant number of linearprogramming problems per facet of the projection in the absence of degeneracy. The ESP algorithm allows us to compute also projected geometric diameters of high-dimensional polytopes. A representation set of projected polytopes is presented to illustrate the methods adopted in this thesis.

The use of quantile trees in the prediction of the diameter distribution of a stand

Abstract

Elemental analysis of wood materials by external millibeam thick target PIXE

PIXE (Particle Induce X-ray Emission spectrometry) was used for analysing stem bark and stem wood of Scots pine, Norway spruce and Silver birch. Thick samples were irradiated, in laboratory atmosphere, with 3 MeV protons and the beam current was measured indirectly using a photo multiplicator (PM) tube. Both point scans and bulk analyses were performed with the 1 mm diameter proton beam. In bulk analyses, whole bark and sectors of discs of the stem wood were dry ashed at 550 ˚C. The ashes were homogenised by shaking and prepared to target pellets for PIXE analyses. This procedure generated representative samples to be analysed, but the enrichment also enabled quantification of some additional trace elements. The ash contents obtained as a product of the sample preparation procedure also showed to be of great importance in the evaluation of results in environmental studies. Spot scans from the pith of pine wood outwards, showed clearly highest concentrations of manganese, calcium and zinc in the first spot irradiated, or 2-3 times higher than in the surrounding wood. For stem wood from the crown part of a pine this higher concentration level was found in the first four spots/mms, including the pith and the two following growth rings. Zinc showed increasing concentrations outwards in sapwood of the pine stem, with the over-all lowest concentrations in the inner half of the sapwood. This could indicate emigration of this element from sapwood being under transformation to heartwood. Point scans across sapwood of pine and spruce showed more distinct variations in concentrations relative to hearth wood. Higher concentrations of e.g. zinc, calcium and manganese were found in earlywood than in denser latewood. Very high concentrations of iron and copper were also seen for some earlywood increments. The ash content of stem bark is up to and order higher than for the stem wood. However, when the elemental concentration in ashes of bark and wood of the same disc were compared, these are very similar – this when trees are growing at spots with no anthropogenic contamination from the atmosphere. The largest difference was obtained for calcium which appeared at two times high concentrations in ashes of bark than in ashes of the wood (ratio of 2). Pine bark is often used in monitoring of atmospheric pollution, where concentrations in bark samples are compared. Here an alternative approach is suggested: Bark and the underlying stem wood of a pine trees are dry ashed and analysed. The elemental concentration in the bark ash is then compared to the concentration of the same element in the wood ash. Comparing bark to wood includes a normalisation for the varying availability of an element from the soil at different sites. When this comparison is done for the ashes of the materials, a normalisation is also obtained for the general and locally different enrichment of inorganic elements from wood to bark. Already a ratio >2 between the concentration in the bark ash and the concentration in the wood ash could indicate atmospheric pollution. For monitoring where bark is used, this way of “inwards” comparison is suggested - instead of comparing to results from analyses of bark from other trees (read reference areas), growing at sites with different soil and, locally, different climate conditions. This approach also enables evaluation of atmospheric pollution from sampling of only relative few individual trees –preferable during forest felling.

Alpha- and gamma-melanocyte stimulating hormones in obesity. A study of the key central areas of metabolic regulation

The melanocortin system is an important regulator of feeding, energy metabolism,and cardiovascular function and it consists of the pro-opiomelanocortin (POMC) derived melanocyte stimulating hormones (α-, β- and γ-MSH) and their endogenous melanocortin receptors, MC1R to MC5R. In the hypothalamus, α-MSH reduces food intake, and increases energy expenditure and sympathetic tone by binding to MC4R. Mutations affecting the MC4R gene lead to obesity in mammals. On the other hand, the metabolic effects of MC3R stimulation using agonists such as the endogenously expressed γ-MSH have been less extensively explored. The main objective of this study was to investigate the long-term effects of increased melanocortin tone in key areas of metabolic regulation in the central nervous system (CNS) in order to investigate the sitespecific roles of both α-MSH and γ-MSH. The aim was to stereotaxically induce local overexpression of single melanocortin peptides using lentiviral vectors expressing α-MSH (LVi-α-MSH-EGFP) and γ-MSH (LVi-γ-MSH-EGFP). The lentiviral vectors were shown to produce a long-term overexpression and biologically active peptides in cell-based assays. The LVi-α-MSHEGFP was targeted to the arcuate nucleus in the hypothalamus of diet induced obese mice where it reduced weight gain and adiposity independently of food intake. When the nucleus tractus solitarus in the brainstem was targeted, the LVi-α-MSH-EGFP treatment was shown to cause a small decrease in adiposity, which did not impact weight development. However, the α-MSH treatment increased heart rate, which was attenuated by adrenergic receptor blockade indicative of increased sympathetic activity. The LVi-γ-MSH-EGFP was targeted to the hypothalamus where it decreased fat mass in mice eating the standard diet, but the effect was abated if animals consumed a high-fat Western type diet. When the diet induced obese mice were subjected again to the standard diet, the LVi-γ-MSH-EGFP treated animals displayed increased weight loss and reduced adiposity. These results indicate that the long-term central anti-obesity effects of α-MSH are independent of food intake. In addition, overexpression of α-MSH in the brain stem efficiently blocked the development of adiposity, but increased sympathetic tone. The evidence presented in this thesis also indicates that selective MC3R agonists such as γ-MSH could be potential therapeutics in combination with low fat diets.

Quantitative Magnetic Resonance Imaging of the Liver and Heart In Iron Overload

Systemic iron overload (IO) is considered a principal determinant in the clinical outcome of different forms of IO and in allogeneic hematopoietic stem cell transplantation (alloSCT). However, indirect markers for iron do not provide exact quantification of iron burden, and the evidence of iron-induced adverse effects in hematological diseases has not been established. Hepatic iron concentration (HIC) has been found to represent systemic IO, which can be quantified safely with magnetic resonance imaging (MRI), based on enhanced transverse relaxation. The iron measurement methods by MRI are evolving. The aims of this study were to implement and optimise the methodology of non-invasive iron measurement with MRI to assess the degree and the role of IO in the patients. An MRI-based HIC method (M-HIC) and a transverse relaxation rate (R2*) from M-HIC images were validated. Thereafter, a transverse relaxation rate (R2) from spin-echo imaging was calibrated for IO assessment. Two analysis methods, visual grading and rSI, for a rapid IO grading from in-phase and out-of-phase images were introduced. Additionally, clinical iron indicators were evaluated. The degree of hepatic and cardiac iron in our study patients and IO as a prognostic factor in patients undergoing alloSCT were explored. In vivo and in vitro validations indicated that M-HIC and R2* are both accurate in the quantification of liver iron. R2 was a reliable method for HIC quantification and covered a wider HIC range than M-HIC and R2*. The grading of IO was able to be performed rapidly with the visual grading and rSI methods. Transfusion load was more accurate than plasma ferritin in predicting transfusional IO. In patients with hematological disorders, the prevalence of hepatic IO was frequent, opposite to cardiac IO. Patients with myelodysplastic syndrome were found to be the most susceptible to IO. Pre-transplant IO predicted severe infections during the early post-transplant period, in contrast to the reduced risk of graft-versus-host disease. Iron-induced, poor transplantation results are most likely to be mediated by severe infections.