Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Carotid Surgery : A posse ad esse non valet consequentia

According to a large body of evidence, carotid endarterectomy (CEA) can prevent strokes, provided that appropriate inclusion criteria and high-quality perioperative treatment methods are utilised with low complication rates. From the patient s perspective, it is of paramount importance that the operation is as safe and effective as possible. From the community s point of view, it is important that CEA provision prevents as many strokes as possible. In order to define the stroke preventing potential of CEA in different communities, a comparison between eight European countries and Australia was performed including 53 077 carotid interventions. A more detailed evaluation was performed in Finland, the United Kingdom and Egypt. It could be estimated that many potentially preventable strokes occur due to insufficient diagnostics and CEA provision. The number of CEAs should be at least doubled in the Helsinki region. The theoretical power of CEA provision in stroke prevention varied significantly between the countries. Delay from symptom to surgery has been identified as one of the most important factors influencing the effectiveness of CEA. In 2008 only 11% of CEAs in Helsinki university central hospital (HUCH) were performed within the recommended14 days. Registered data of 673 CEAs in HUCH during 2000-2005 was analyzed. There was no systematic error that would have changed the outcome analysis. However it is important that registers are audited regularly and cross matching of different registries is possible. A previously unpublished method of combining medial mandibulotomy, neck incision and carotid artery interposition was carried out as a collaboration of maxillofacial, ear, nose and throat and vascular surgeons. Five patients were operated on with a technique that was feasible and possible to perform with little morbidity, but due to the significant risks involved, this technique should be reserved for carefully selected cases. In stroke prevention, organisational decisions seem far more important than details in interventional procedures when CEA is performed with low complication rates, as was the case in the present study. A TIA clinic approach with close co-operation between the on-call vascular surgeons, neurologists and radiologists should be available at all centres treating these patients. Patients should have a direct and fast admission to the hospital performing CEA.

Molecular profiling of indoor microbial communities in moisture damaged and non-damaged buildings

Epidemiological studies have shown an elevation in the incidence of asthma, allergic symptoms and respiratory infections among people living or working in buildings with moisture and mould problems. Microbial growth is suspected to have a key role, since the severity of microbial contamination and symptoms show a positive correlation, while the removal of contaminated materials relieves the symptoms. However, the cause-and-effect relationship has not been well established and knowledge of the causative agents is incomplete. The present consensus of indoor microbes relies on culture-based methods. Microbial cultivation and identification is known to provide qualitatively and quantitatively biased results, which is suspected to be one of the reasons behind the often inconsistent findings between objectively measured microbiological attributes and health. In the present study the indoor microbial communities were assessed using culture-independent, DNA based methods. Fungal and bacterial diversity was determined by amplifying and sequencing the nucITS- and16S-gene regions, correspondingly. In addition, the cell equivalent numbers of 69 mould species or groups were determined by quantitative PCR (qPCR). The results from molecular analyses were compared with results obtained using traditional plate cultivation for fungi. Using DNA-based tools, the indoor microbial diversity was found to be consistently higher and taxonomically wider than viable diversity. The dominant sequence types of fungi, and also of bacteria were mainly affiliated with well-known microbial species. However, in each building they were accompanied by various rare, uncultivable and unknown species. In both moisture-damaged and undamaged buildings the dominant fungal sequence phylotypes were affiliated with the classes Dothideomycetes (mould-like filamentous ascomycetes); Agaricomycetes (mushroom- and polypore-like filamentous basidiomycetes); Urediniomycetes (rust-like basidiomycetes); Tremellomycetes and the family Malasseziales (both yeast-like basidiomycetes). The most probable source for the majority of fungal types was the outdoor environment. In contrast, the dominant bacterial phylotypes in both damaged and undamaged buildings were affiliated with human-associated members within the phyla Actinobacteria and Firmicutes. Indications of elevated fungal diversity within potentially moisture-damage-associated fungal groups were recorded in two of the damaged buildings, while one of the buildings was characterized by an abundance of members of the Penicillium chrysogenum and P. commune species complexes. However, due to the small sample number and strong normal variation firm conclusions concerning the effect of moisture damage on the species diversity could not be made. The fungal communities in dust samples showed seasonal variation, which reflected the seasonal fluctuation of outdoor fungi. Seasonal variation of bacterial communities was less clear but to some extent attributable to the outdoor sources as well. The comparison of methods showed that clone library sequencing was a feasible method for describing the total microbial diversity, indicated a moderate quantitative correlation between sequencing and qPCR results and confirmed that culture based methods give both a qualitative and quantitative underestimate of microbial diversity in the indoor environment. However, certain important indoor fungi such as Penicillium spp. were clearly underrepresented in the sequence material, probably due to their physiological and genetic properties. Species specific qPCR was a more efficient and sensitive method for detecting and quantitating individual species than sequencing, but in order to exploit the full advantage of the method in building investigations more information is needed about the microbial species growing on damaged materials. In the present study, a new method was also developed for enhanced screening of the marker gene clone libraries. The suitability of the screening method to different kinds of microbial environments including biowaste compost material and indoor settled dusts was evaluated. The usability was found to be restricted to environments that support the growth and subsequent dominance of a small number microbial species, such as compost material.

Professional non-neutrality: criticising the third party in psychotherapy

Using audio-recorded data from cognitive-constructivist psychotherapy, the article shows a particular institutional context in which successful professional action does not adhere to the pattern of affective neutrality which Parsons saw as an inherent component of medicine and psychotherapy. In our data, the professional’s non-neutrality functions as a tool for achieving institutional goals. The analysis focuses on the psychotherapist’s actions that convey a critical stance towards a third party with whom the patient has experienced problems. The data analysis revealed two practices of this kind of critique: (1) the therapist can confirm the critique that the patient has expressed or (2) return to the critique from which the patient has focused away. These actions are shown to build grounds for the therapist’s further actions that challenge the patient’s dysfunctional beliefs. The article suggests that in the case of psychotherapy, actions that as such might be seen as apparent lapses from the neutral professional role can in their specific context perform the task of the institution at hand.