Convex-transitive Banach spaces and their hyperplanes

The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.

Molecular classification of familial colorectal and endometrial carcinoma

Hereditary nonpolyposis colorectal cancer (HNPCC) is the most common known clearly hereditary cause of colorectal and endometrial cancer (CRC and EC). Dominantly inherited mutations in one of the known mismatch repair (MMR) genes predispose to HNPCC. Defective MMR leads to an accumulation of mutations especially in repeat tracts, presenting microsatellite instability. HNPCC is clinically a very heterogeneous disease. The age at onset varies and the target tissue may vary. In addition, families that fulfill the diagnostic criteria for HNPCC but fail to show any predisposing mutation in MMR genes exist. Our aim was to evaluate the genetic background of familial CRC and EC. We performed comprehensive molecular and DNA copy number analyses of CRCs fulfilling the diagnostic criteria for HNPCC. We studied the role of five pathways (MMR, Wnt, p53, CIN, PI3K/AKT) and divided the tumors into two groups, one with MMR gene germline mutations and the other without. We observed that MMR proficient familial CRC consist of two molecularly distinct groups that differ from MMR deficient tumors. Group A shows paucity of common molecular and chromosomal alterations characteristic of colorectal carcinogenesis. Group B shows molecular features similar to classical microsatellite stable tumors with gross chromosomal alterations. Our finding of a unique tumor profile in group A suggests the involvement of novel predisposing genes and pathways in colorectal cancer cohorts not linked to MMR gene defects. We investigated the genetic background of familial ECs. Among 22 families with clustering of EC, two (9%) were due to MMR gene germline mutations. The remaining familial site-specific ECs are largely comparable with HNPCC associated ECs, the main difference between these groups being MMR proficiency vs. deficiency. We studied the role of PI3K/AKT pathway in familial ECs as well and observed that PIK3CA amplifications are characteristic of familial site-specific EC without MMR gene germline mutations. Most of the high-level amplifications occurred in tumors with stable microsatellites, suggesting that these tumors are more likely associated with chromosomal rather than microsatellite instability and MMR defect. The existence of site-specific endometrial carcinoma as a separate entity remains equivocal until predisposing genes are identified. It is possible that no single highly penetrant gene for this proposed syndrome exists, it may, for example be due to a combination of multiple low penetrance genes. Despite advances in deciphering the molecular genetic background of HNPCC, it is poorly understood why certain organs are more susceptible than others to cancer development. We found that important determinants of the HNPCC tumor spectrum are, in addition to different predisposing germline mutations, organ specific target genes and different instability profiles, loss of heterozygosity at MLH1 locus, and MLH1 promoter methylation. This study provided more precise molecular classification of families with CRC and EC. Our observations on familial CRC and EC are likely to have broader significance that extends to sporadic CRC and EC as well.

Functional outcome and health-related quality of life after traumatic brain injury in the framework of the International Classification of Functioning, Disability and Health (ICF)

Traumatic brain injury (TBI) affects people of all ages and is a cause of long-term disability. In recent years, the epidemiological patterns of TBI have been changing. TBI is a heterogeneous disorder with different forms of presentation and highly individual outcome regarding functioning and health-related quality of life (HRQoL). The meaning of disability differs from person to person based on the individual s personality, value system, past experience, and the purpose he or she sees in life. Understanding of all these viewpoints is needed in comprehensive rehabilitation. This study examines the epidemiology of TBI in Finland as well as functioning and HRQoL after TBI, and compares the subjective and objective assessments of outcome. The frame of reference is the International Classification of Functioning, Disability and Health (ICF). The subjects of Study I represent the population of Finnish TBI patients who experienced their first TBI between 1991 and 2005. The 55 Finnish subjects of Studies II and IV participated in the first wave of the international Quality of life after brain injury (QOLIBRI) validation study. The 795 subjects from six language areas of Study III formed the second wave of the QOLIBRI validation study. The average annual incidence of Finnish hospitalised TBI patients during the years 1991-2005 was 101:100 000 in patients who had TBI as the primary diagnosis and did not have a previous TBI in their medical history. Males (59.2%) were at considerably higher risk of getting a TBI than females. The most common external cause of the injury was falls in all age groups. The number of TBI patients ≥ 70 years of age increased by 59.4% while the number of inhabitants older than 70 years increased by 30.3% in the population of Finland during the same time period. The functioning of a sample of 55 persons with TBI was assessed by extracting information from the patients medical documents using the ICF checklist. The most common problems were found in the ICF components of Body Functions (b) and Activities and Participation (d). HRQoL was assessed with the QOLIBRI which showed the highest level of satisfaction on the Emotions, Physical Problems and Daily Life and Autonomy scales. The highest scores were obtained by the youngest participants and participants living independently without the help of other people, and by people who were working. The relationship between the functional outcome and HRQoL was not straightforward. The procedure of linking the QOLIBRI and the GOSE to the ICF showed that these two outcome measures cover the relevant domains of TBI patients functioning. The QOLIBRI provides the patients subjective view, while the GOSE summarises the objective elements of functioning. Our study indicates that there are certain domains of functioning that are not traditionally sufficiently documented but are important for the HRQoL of persons with TBI. This was the finding especially in the domains of interpersonal relationships, social and leisure activities, self, and the environment. Rehabilitation aims to optimize functioning and to minimize the experience of disability among people with health conditions, and it needs to be based on a comprehensive understanding of human functioning. As an integrative model, the ICF may serve as a frame of reference in achieving such an understanding.

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.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.