Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Root system traits of Norway spruce, Scots pine, and silver birch in mixed boreal forests: an analysis of root architecture, morphology, and anatomy

The aim of this thesis was to unravel the functional-structural characteristics of root systems of Betula pendula Roth., Picea abies (L.) Karst., and Pinus sylvestris L. in mixed boreal forest stands differing in their developmental stage and site fertility. The root systems of these species had similar structural regularities: horizontally-oriented shallow roots defined the horizontal area of influence, and within this area, each species placed fine roots in the uppermost soil layers, while sinker roots defined the maximum rooting depth. Large radial spread and high ramification of coarse roots, and the high specific root length (SRL) and root length density (RLD) of fine roots indicated the high belowground competitiveness and root plasticity of B. pendula. Smaller radial root spread and sparser branching of coarse roots, and low SRL and RLD of fine roots of the conifers could indicate their more conservative resource use and high association with and dependence on ectomycorrhiza-forming fungi. The vertical fine root distributions of the species were mostly overlapping, implying the possibility for intense belowground competition for nutrients. In each species, conduits tapered and their frequency increased from distal roots to the stem, from the stem to the branches, and to leaf petioles in B. pendula. Conduit tapering was organ-specific in each species violating the assumptions of the general vascular scaling model (WBE). This reflects the hierarchical organization of a tree and differences between organs in the relative importance of transport, safety, and mechanical demands. The applied root model was capable of depicting the mass, length and spread of coarse roots of B. pendula and P. abies, and to the lesser extent in P. sylvestris. The roots did not follow self-similar fractal branching, because the parameter values varied within the root systems. Model parameters indicate differences in rooting behavior, and therefore different ecophysiological adaptations between species.

Mid-urethral slings for treatment of stress urinary incontinence : long- and mid-term follow-up

Urinary incontinence is a common problem, affecting one third of the women at least at some time during their lives. The prevalence of urinary incontinence increases with advancing age, and the everyday impact of incontinence on women and on health services is enormous. Urinary incontinence is usually divided into three different subtypes, of which stress urinary incontinence (SUI) is the most common. Surgical treatment is often needed to cure SUI, and modern mid-urethral sling procedures give the possibility to cure this condition with a low risk of adverse events, a problem often associated with the so-called traditional incontinence operations. Life expectancy among women in Western countries has grown beyond 80 years of age. Long-term efficacy of treatment options for urinary incontinence therefore becomes an important issue in a world with limited eco-nomic resources. The purpose of the present study was to prospectively evaluate the long-term efficacy and safety of the first minimally invasive mid-urethral tape procedure, the Tension-free Vaginal Tape (TVT) procedure. The long-term (5-year) follow-up results of the TVT procedure as a repeat operation af-ter an unsuccessful mid-urethral tape operation were studied and the reasons for failure of the first operation were analyzed. Another purpose was to compare the original TVT procedure with a newer modification, the Tension-free Vaginal Tape Obturator (TVT-O) procedure within a multi-centre, randomized context in order to find out possible differences between these procedures re-garding efficacy and complications and the effects on symptoms of urgency. The first study of the present thesis is a prospective, Nordic, three-centre follow-up study of 90 women suffering from SUI, who were treated by means of the TVT procedure. The mean follow-up time was more than eleven years, and the study is the first to be published in connection with more than ten years of follow-up. The second study is a retrospective analysis of 26 women who were treated with a repeat TVT procedure after an unsuccessful primary mid-urethral tape procedure. The third and fourth studies concern 273 women in seven centres in Finland who were ran-domly assigned to the TVT and TVT-O procedures, the 3-year follow-up results of which are pre-sented in this thesis. After eleven years of follow-up, 90% of the women had a negative cough stress test result and a negative 24-h pad test result. The subjective cure rate measured as the women s global impression of cure was 77%, the rate of improvement 20%, and only 3% thought that the treatment had failed. No late-onset adverse effects were found. The repeat TVT procedure was successful in 75% of the cases when women who were cured and women who were significantly improved were included. The reasons for failure of the first operation could be separated into four different groups: tape material-related, operation technique-related, concomitant illness-related and a group with no identifiable reason. There were no intra-operative complications during the repeat operation. In the randomized trial comparing the TVT with the TVT-O procedure a cough stress test results were negative in 94.6% and 89.5% of the women in the two groups, respectively, after a 3-year follow-up period. There were no statistical differences in the cure rate or the rate of complications be-tween the two procedures. Symptoms of urgency were analyzed more closely and the main finding was that the prevalence of urgency symptoms decreased significantly after both mid-urethral sling procedures. The TVT operation was found to be an effective and safe procedure even after eleven years of follow-up. Long-term follow-up after a repeat TVT procedure revealed that the TVT procedure can well be considered after an unsuccessful mid-urethra tape procedure, because 75% of the patients showed significantly improvement of their incontinence. The TVT and TVT-O procedures showed no statistically significant differences in efficacy and rate of complications after three years of follow-up. In most cases these procedures alleviate preoperative symptoms of urgency and the risk of developing de novo urgency is low.