Space in Musical Semiosis : An Abductive Theory of the Musical Composition Process

Space in musical semiosis is a study of musical meaning, spatiality and composition. Earlier studies on musical composition have not adequately treated the problems of musical signification. Here, composition is considered an epitomic process of musical signification. Hence the core problems of composition theory are core problems of musical semiotics. The study employs a framework of naturalist pragmatism, based on C. S. Peirce’s philosophy. It operates on concepts such as subject, experience, mind and inquiry, and incorporates relevant ideas of Aristotle, Peirce and John Dewey into a synthetic view of esthetic, practic, and semiotic for the benefit of grasping musical signification process as a case of semiosis in general. Based on expert accounts, music is depicted as real, communicative, representational, useful, embodied and non-arbitrary. These describe how music and the musical composition process are mental processes. Peirce’s theories are combined with current morphological theories of cognition into a view of mind, in which space is central. This requires an analysis of space, and the acceptance of a relativist understanding of spatiality. This approach to signification suggests that mental processes are spatially embodied, by virtue of hard facts of the world, literal representations of objects, as well as primary and complex metaphors each sharing identities of spatial structures. Consequently, music and the musical composition process are spatially embodied. Composing music appears as a process of constructing metaphors—as a praxis of shaping and reshaping features of sound, representable from simple quality dimensions to complex domains. In principle, any conceptual space, metaphorical or literal, may set off and steer elaboration, depending on the practical bearings on the habits of feeling, thinking and action, induced in musical communication. In this sense, it is evident that music helps us to reorganize our habits of feeling, thinking, and action. These habits, in turn, constitute our existence. The combination of Peirce and morphological approaches to cognition serves well for understanding musical and general signification. It appears both possible and worthwhile to address a variety of issues central to musicological inquiry in the framework of naturalist pragmatism. The study may also contribute to the development of Peircean semiotics.

Familial aggregation of type 1 diabetes and diabetic nephropathy in Finland

Type 1 diabetes (T1D) is a common, multifactorial disease with strong familial clustering. In Finland, the incidence of T1D among children aged 14 years or under is the highest in the world. The increase in incidence has been approximately 2.4% per year. Although most new T1D cases are sporadic the first-degree relatives are at an increased risk of developing the same disease. This study was designed to examine the familial aggregation of T1D and one of its serious complications, diabetic nephropathy (DN). More specifically the study aimed (1) to determine the concordance rates of T1D in monozygotic (MZ) and dizygotic (DZ) twins and to estimate the relative contributions of genetic and environmental factors to the variability in liability to T1D as well as to study the age at onset of diabetes in twins; (2) to obtain long-term empirical estimates of the risk of T1D among siblings of T1D patients and the factors related to this risk, especially the effect of age at onset of diabetes in the proband and the birth cohort effect; (3) to establish if DN is aggregating in a Finnish population-based cohort of families with multiple cases of T1D, and to assess its magnitude and particularly to find out whether the risk of DN in siblings is varying according to the severity of DN in the proband and/or the age at onset of T1D: (4) to assess the recurrence risk of T1D in the offspring of a Finnish population-based cohort of patients with childhood onset T1D, and to investigate potential sex-related effects in the transmission of T1D from the diabetic parents to their offspring as well as to study whether there is a temporal trend in the incidence. The study population comprised of the Finnish Young Twin Cohort (22,650 twin pairs), a population-based cohort of patients with T1D diagnosed at the age of 17 years or earlier between 1965 and 1979 (n=5,144) and all their siblings (n=10,168) and offspring (n=5,291). A polygenic, multifactorial liability model was fitted to the twin data. Kaplan-Meier analyses were used to provide the cumulative incidence for the development of T1D and DN. Cox s proportional hazards models were fitted to the data. Poisson regression analysis was used to evaluate temporal trends in incidence. Standardized incidence ratios (SIRs) between the first-degree relatives of T1D patients and background population were determined. The twin study showed that the vast majority of affected MZ twin pairs remained discordant. Pairwise concordance for T1D was 27.3% in MZ and 3.8% in DZ twins. The probandwise concordance estimates were 42.9% and 7.4%, respectively. The model with additive genetic and individual environmental effects was the best-fitting liability model to T1D, with 88% of the phenotypic variance due to genetic factors. The second paper showed that the 50-year cumulative incidence of T1D in the siblings of diabetic probands was 6.9%. A young age at diagnosis in the probands considerably increased the risk. If the proband was diagnosed at the age of 0-4, 5-9, 10-14, 15 or more, the corresponding 40-year cumulative risks were 13.2%, 7.8%, 4.7% and 3.4%. The cumulative incidence increased with increasing birth year. However, SIR among children aged 14 years or under was approximately 12 throughout the follow-up. The third paper showed that diabetic siblings of the probands with nephropathy had a 2.3 times higher risk of DN compared with siblings of probands free of nephropathy. The presence of end stage renal disease (ESRD) in the proband increases the risk three-fold for diabetic siblings. Being diagnosed with diabetes during puberty (10-14) or a few years before (5-9) increased the susceptibility for DN in the siblings. The fourth paper revealed that of the offspring of male probands, 7.8% were affected by the age of 20 compared with 5.3% of the offspring of female probands. Offspring of fathers with T1D have 1.7 times greater risk to be affected with T1D than the offspring of mothers with T1D. The excess risk in the offspring of male fathers manifested itself through the higher risk the younger the father was when diagnosed with T1D. Young age at onset of diabetes in fathers increased the risk of T1D greatly in the offspring, but no such pattern was seen in the offspring of diabetic mothers. The SIR among offspring aged 14 years or under remained fairly constant throughout the follow-up, approximately 10. The present study has provided new knowledge on T1D recurrence risk in the first-degree relatives and the risk factors modifying the risk. Twin data demonstrated high genetic liability for T1D and increased heritability. The vast majority of affected MZ twin pairs, however, remain discordant for T1D. This study confirmed the drastic impact of the young age at onset of diabetes in the probands on the increased risk of T1D in the first-degree relatives. The only exception was the absence of this pattern in the offspring of T1D mothers. Both the sibling and the offspring recurrence risk studies revealed dynamic changes in the cumulative incidence of T1D in the first-degree relatives. SIRs among the first-degree relatives of T1D patients seems to remain fairly constant. The study demonstrates that the penetrance of the susceptibility genes for T1D may be low, although strongly influenced by the environmental factors. Presence of familial aggregation of DN was confirmed for the first time in a population-based study. Although the majority of the sibling pairs with T1D were discordant for DN, its presence in one sibling doubles and presence of ESRD triples the risk of DN in the other diabetic sibling. An encouraging observation was that although the proportion of children to be diagnosed with T1D at the age of 4 or under is increasing, they seem to have a decreased risk of DN or at least delayed onset.

Early growth and adult health: focus on blood pressure, glucose tolerance status and body composition

Theory of developmental origins of adult health and disease proposes that experiences during critical periods of early development may have consequences on health throughout a lifespan. Thesis studies aimed to characterize associations between early growth and some components of the metabolic syndrome cluster. Participants belong to two epidemiological cohorts with data on birth measurements and, for the younger cohort, on serial recordings of weight and height during childhood. They were born as singletons between 1924-33 and 1934-44 in the Helsinki University Central Hospital, and 500 and 2003 of them, respectively, attended clinical studies at the age of 65-75 and 56-70 years, respectively. In the 65-75 year old men and women, the well-known inverse relationship between birth weight and systolic blood pressure (SBP) was confined to people who had established hypertension. Among them a 1-kg increase in birth weight was associated with a 6.4-mmHg (95% CI: 1.0 to 11.9) decrease in SBP. This relationship was further confined to people with the prevailing Pro12Pro polymorphism of the peroxisome proliferator-activated receptor-γ2 (PPARγ2) gene. People with low birth weight were more likely to receive angiotensin-converting enzyme inhibitors/angiotensin-receptor blockers (ACEI/ARB, p=0.03), and, again, this relationship was confined to the carriers of the Pro12Pro (p=0.01 for interaction). These results suggest that the inverse association between birth weight and systolic BP becomes focused in hypertensive people because pathological features of BP regulation, associated with slow fetal growth, become self-perpetuating in adult life. Insulin resistance of the Pro12Pro carriers with low birth weight may interact with the renin-angiotensin system leading to raised BP levels. Habitual physical activity protected men and women who were small at birth, and thus at increased risk for the development of type 2 diabetes, against glucose intolerance more strongly. Among subjects with birth weight ≤3000 g, the odds ratio (OR) for glucose intolerance was 5.2 (95% CI: 2.1 to 13) in those who exercised less than 3 times per week compared to regular exercisers; in those who scored their exercise light compared with moderate exercisers (defined as comparable to brisk walking) the OR was 3.5 (1.5 to 8.2). In the 56-70 year old men a 1 kg increase in birth weight corresponded to a 4.1 kg (95% CI: 3.1 to 5.1) and in women to a 2.9 kg (2.1 to 3.6) increase in adult lean mass. Rapid gain in body mass index (BMI), i.e. crossing from an original BMI percentile to a higher one, before the age of 2 years increased adult lean mass index (LMI, lean mass/height squared) without excess fat accumulation whereas rapid gain in BMI during later childhood, despite the concurrent rise in LMI, resulted in a relatively higher increase in adult body fat mass. These findings illustrate how genes, the environment and their interactions, early growth patterns, and adult lifestyle modify adult health risks which originate from early life.

Prevention of type 2 diabetes with lifestyle intervention - emphasis on dietary composition and identification of high-risk individuals

Type 2 diabetes is an increasing, serious, and costly public health problem. The increase in the prevalence of the disease can mainly be attributed to changing lifestyles leading to physical inactivity, overweight, and obesity. These lifestyle-related risk factors offer also a possibility for preventive interventions. Until recently, proper evidence regarding the prevention of type 2 diabetes has been virtually missing. To be cost-effective, intensive interventions to prevent type 2 diabetes should be directed to people at an increased risk of the disease. The aim of this series of studies was to investigate whether type 2 diabetes can be prevented by lifestyle intervention in high-risk individuals, and to develop a practical method to identify individuals who are at high risk of type 2 diabetes and would benefit from such an intervention. To study the effect of lifestyle intervention on diabetes risk, we recruited 522 volunteer, middle-aged (aged 40 - 64 at baseline), overweight (body mass index > 25 kg/m2) men (n = 172) and women (n = 350) with impaired glucose tolerance to the Diabetes Prevention Study (DPS). The participants were randomly allocated either to the intensive lifestyle intervention group or the control group. The control group received general dietary and exercise advice at baseline, and had annual physician's examination. The participants in the intervention group received, in addition, individualised dietary counselling by a nutritionist. They were also offered circuit-type resistance training sessions and were advised to increase overall physical activity. The intervention goals were to reduce body weight (5% or more reduction from baseline weight), limit dietary fat (< 30% of total energy consumed) and saturated fat (< 10% of total energy consumed), and to increase dietary fibre intake (15 g / 1000 kcal or more) and physical activity (≥ 30 minutes/day). Diabetes status was assessed annually by a repeated 75 g oral glucose tolerance testing. First analysis on end-points was completed after a mean follow-up of 3.2 years, and the intervention phase was terminated after a mean duration of 3.9 years. After that, the study participants continued to visit the study clinics for the annual examinations, for a mean of 3 years. The intervention group showed significantly greater improvement in each intervention goal. After 1 and 3 years, mean weight reductions were 4.5 and 3.5 kg in the intervention group and 1.0 kg and 0.9 kg in the control group. Cardiovascular risk factors improved more in the intervention group. After a mean follow-up of 3.2 years, the risk of diabetes was reduced by 58% in the intervention group compared with the control group. The reduction in the incidence of diabetes was directly associated with achieved lifestyle goals. Furthermore, those who consumed moderate-fat, high-fibre diet achieved the largest weight reduction and, even after adjustment for weight reduction, the lowest diabetes risk during the intervention period. After discontinuation of the counselling, the differences in lifestyle variables between the groups still remained favourable for the intervention group. During the post-intervention follow-up period of 3 years, the risk of diabetes was still 36% lower among the former intervention group participants, compared with the former control group participants. To develop a simple screening tool to identify individuals who are at high risk of type 2 diabetes, follow-up data of two population-based cohorts of 35-64 year old men and women was used. The National FINRISK Study 1987 cohort (model development data) included 4435 subjects, with 182 new drug-treated cases of diabetes identified during ten years, and the FINRISK Study 1992 cohort (model validation data) included 4615 subjects, with 67 new cases of drug-treated diabetes during five years, ascertained using the Social Insurance Institution's Drug register. Baseline age, body mass index, waist circumference, history of antihypertensive drug treatment and high blood glucose, physical activity and daily consumption of fruits, berries or vegetables were selected into the risk score as categorical variables. In the 1987 cohort the optimal cut-off point of the risk score identified 78% of those who got diabetes during the follow-up (= sensitivity of the test) and 77% of those who remained free of diabetes (= specificity of the test). In the 1992 cohort the risk score performed equally well. The final Finnish Diabetes Risk Score (FINDRISC) form includes, in addition to the predictors of the model, a question about family history of diabetes and the age category of over 64 years. When applied to the DPS population, the baseline FINDRISC value was associated with diabetes risk among the control group participants only, indicating that the intensive lifestyle intervention given to the intervention group participants abolished the diabetes risk associated with baseline risk factors. In conclusion, the intensive lifestyle intervention produced long-term beneficial changes in diet, physical activity, body weight, and cardiovascular risk factors, and reduced diabetes risk. Furthermore, the effects of the intervention were sustained after the intervention was discontinued. The FINDRISC proved to be a simple, fast, inexpensive, non-invasive, and reliable tool to identify individuals at high risk of type 2 diabetes. The use of FINDRISC to identify high-risk subjects, followed by lifestyle intervention, provides a feasible scheme in preventing type 2 diabetes, which could be implemented in the primary health care system.

Immunodeficiencies, pathogens and sex in upper respiratory diseases

In the first part of this thesis the association of different forms of sinonasal diseases and plasma concentrations of C3, C4, immunoglobulins, immunoglobulin G subclasses, C4A and C4B gene numbers were studied in 287 adult patients and 150 sex-matched adult controls. Patients were well characterized and stratified into groups using strict clinical criteria and females and males were also studied as separate groups. Severe primary antibody antibody deficiencies were rare in patients coming to sinonasal operations. Female patients had more recurrent sinusitis and other mucosal infections and males had more nasal polyposis. Upregulation of complement activity was seen in acute rhinosinusitis patients (high levels of plasma C3, C4, and complement classical pathway activity CH50) and male patients coming to sinonasal operations (high levels of plasma C3 and C4). In females, total and partial C4B deficiencies and lower levels of IgG1 and IgG3 were associated with rhinosinusitis leading to sinonasal operations. C4A deficiencies were found to predispose to severe chronic rhinosinusitis in females and males. In female patients with chronic or recurrent rhinosinusitis with nasal polyposis C4B deficiencies seem to predispose to the disease, but in males with a similar disease C4B deficiencies seem to be protective. This suggests a different pathophysiology between sexes in this form of sinonasal disease. In the second part of this thesis work 213 children coming to elective tonsillectomy were studied and compared with 155 randomly selected school children. An association with recurrent upper respiratory tract infections and hypersensitivity disorders was seen especially in children under 7 years of age. However, this association was not seen in levels of specific IgE to respiratory allergens in the same age group. Both symptomatic respiratory allergy and specific IgE to respiratory allergens became more common in boys than girls over 7 years of age. We were able to show that although both rhinoviruses and bacterial pathogens were found in the tonsils, no association between their presence and clinical forms of tonsillar disease was seen. The ability of GAS to bind complement regulators FH and C4BP did not differ between strains causing tonsillar diseases or septicemia, suggesting that other virulence mechanisms of the bacteria are more important.

Genetics of Cardiovascular Disease: A Candidate Gene Study of USF1

Cardiovascular diseases (CVD) are major contributors to morbidity and mortality worldwide. Several interacting environmental, biochemical, and genetic risk factors can increase disease susceptibility. While some of the genes involved in the etiology of CVD are known, many are yet to be discovered. During the last few decades, scientists have searched for these genes with genome-wide linkage and association methods, and with more targeted candidate gene studies. This thesis investigates variation within the upstream transcription factor 1 (USF1) gene locus in relation to CVD risk factors, atherosclerosis, and incidence and prevalence of CVD. This candidate gene was first identified in Finnish families ascertained for familial combined hyperlipidemia, a common dyslipidemia predisposing to coronary heart disease. The gene is a ubiquitously expressed transcription factor regulating expression of several genes from lipid and glucose metabolism, inflammation, and endothelial function. First, we examined association between USF1 variants and several CVD risk factors, such as lipid phenotypes, body composition measures, and metabolic syndrome, in two prospective population cohorts. Our data suggested that USF1 contributes to these CVD risk factors at the population level. Notably, the associations with quantitative measurements were mostly detected among study subjects with CVD or metabolic syndrome, suggesting complex interactions between USF1 effects and the pathophysiological state of an individual. Second, we investigated how variation at the USF1 locus contributes to atherosclerotic lesions of the coronary arteries and abdominal aorta. For this, we used two study samples of middle-aged men with detailed measurements of atherosclerosis obtained in autopsy. USF1 variation significantly associated with areas of several types of lesions, especially with calcification of the arteries. Next, we tested what effect the USF1 risk variants have on sudden cardiac death and incidence of CVD. The atherosclerosis-associated risk variant increased the risk of sudden cardiac death of the same study subjects. Furthermore, USF1 alleles associated with incidence of CVD in the Finnish population follow-up cohorts. These associations were especially prominent among women, suggesting a sex specific effect, which has also been detected in subsequent studies. Finally, as some of the low-yield DNA samples of the Finnish follow-up study cohort needed to be whole-genome amplified (WGA) prior to genotyping, we evaluated whether the produced WGA genotypes were of good quality. Although the samples giving genotype discrepancies could not be detected before genotyping with standard laboratory quality control methods, our results suggested that enhanced quality control at the time of the genotyping could identify such samples. In addition, combining two WGA reactions into one pooled DNA sample for genotyping markedly reduced the number of discrepancies and samples showing them. In conclusion, USF1 seems to have a role in the etiology of CVD. Additional studies are warranted to identify functional variants and to study interactions between USF1 and other genetic or environmental factors. This USF1 study, and other studies with low DNA yield of some samples, can benefit from whole genome amplification of the low-yield samples prior to genotyping. Careful quality control procedures are, however, needed in WGA genotyping.

A dynamic programming model for optimising feeding and slaughter decisions regarding fattening pigs

Costs of purchasing new piglets and of feeding them until slaughter are the main variable expenditures in pig fattening. They both depend on slaughter intensity, the nature of feeding patterns and the technological constraints of pig fattening, such as genotype. Therefore, it is of interest to examine the effect of production technology and changes in input and output prices on feeding and slaughter decisions. This study examines the problem by using a dynamic programming model that links genetic characteristics of a pig to feeding decisions and the timing of slaughter and takes into account how these jointly affect the quality-adjusted value of a carcass. The model simulates the growth mechanism of a pig under optional feeding and slaughter patterns and then solves the optimal feeding and slaughter decisions recursively. The state of nature and the genotype of a pig are known in the analysis. The main contribution of this study is the dynamic approach that explicitly takes into account carcass quality while simultaneously optimising feeding and slaughter decisions. The method maximises the internal rate of return to the capacity unit. Hence, the results can have vital impact on competitiveness of pig production, which is known to be quite capital-intensive. The results suggest that producer can significantly benefit from improvements in the pig's genotype, because they improve efficiency of pig production. The annual benefits from obtaining pigs of improved genotype can be more than €20 per capacity unit. The annual net benefits of animal breeding to pig farms can also be considerable. Animals of improved genotype can reach optimal slaughter maturity quicker and produce leaner meat than animals of poor genotype. In order to fully utilise the benefits of animal breeding, the producer must adjust feeding and slaughter patterns on the basis of genotype. The results suggest that the producer can benefit from flexible feeding technology. The flexible feeding technology segregates pigs into groups according to their weight, carcass leanness, genotype and sex and thereafter optimises feeding and slaughter decisions separately for these groups. Typically, such a technology provides incentives to feed piglets with protein-rich feed such that the genetic potential to produce leaner meat is fully utilised. When the pig approaches slaughter maturity, the share of protein-rich feed in the diet gradually decreases and the amount of energy-rich feed increases. Generally, the optimal slaughter weight is within the weight range that pays the highest price per kilogram of pig meat. The optimal feeding pattern and the optimal timing of slaughter depend on price ratios. Particularly, an increase in the price of pig meat provides incentives to increase the growth rates up to the pig's biological maximum by increasing the amount of energy in the feed. Price changes and changes in slaughter premium can also have large income effects. Key words: barley, carcass composition, dynamic programming, feeding, genotypes, lean, pig fattening, precision agriculture, productivity, slaughter weight, soybeans

Chemical mass closure and source-specific composition of atmospheric particles

It has been known for decades that particles can cause adverse health effects as they are deposited within the respiratory system. Atmospheric aerosol particles influence climate by scattering solar radiation but aerosol particles act also as the nuclei around which cloud droplets form. The principal objectives of this thesis were to investigate the chemical composition and the sources of fine particles in different environments (traffic, urban background, remote) as well as during some specific air pollution situations. Quantifying the climate and health effects of atmospheric aerosols is not possible without detailed information of the aerosol chemical composition. Aerosol measurements were carried out at nine sites in six countries (Finland, Germany, Czech, Netherlands, Greece and Italy). Several different instruments were used in order to measure both the particulate matter (PM) mass and its chemical composition. In the off-line measurements the samples were collected first on a substrate or filter and gravimetric and chemical analysis were conducted in the laboratory. In the on-line measurements the sampling and analysis were either a combined procedure or performed successively within the same instrument. Results from the impactor samples were analyzed by the statistical methods. This thesis comprises also a work where a method for the determination carbonaceous matter size distribution by using a multistage impactor was developed. It was found that the chemistry of PM has usually strong spatial, temporal and size-dependent variability. In the Finnish sites most of the fine PM consisted of organic matter. However, in Greece sulfate dominated the fine PM and in Italy nitrate made the largest contribution to the fine PM. Regarding the size-dependent chemical composition, organic components were likely to be enriched in smaller particles than inorganic ions. Data analysis showed that organic carbon (OC) had four major sources in Helsinki. Secondary production was the major source in Helsinki during spring, summer and fall, whereas in winter biomass combustion dominated OC. The significant impact of biomass combustion on OC concentrations was also observed in the measurements performed in Central Europe. In this thesis aerosol samples were collected mainly by the conventional filter and impactor methods which suffered from the long integration time. However, by filter and impactor measurements chemical mass closure was achieved accurately, and a simple filter sampling was found to be useful in order to explain the sources of PM on the seasonal basis. The online instruments gave additional information related to the temporal variations of the sources and the atmospheric mixing conditions.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.