Ancient Philosophers on Mental Illness

This dissertation is about ancient philosophers notions of mental illness, from Plato onwards. Mental illness here means disorders that, in ancient medical thought, were believed to originate in the body but to manifest themselves predominantly through mental symptoms. These illnesses were treated by physical means, which were believed to address the bodily cause of the illness, conceived of as an elemental imbalance or a state of cephalic stricture , for example. Sometimes the mental symptoms were addressed directly by psychotherapeutic means. The first and most important question explored concerns how the ancient philosophers responded to the medical notion of mental illness, and how they explained such illnesses in their theories of physiology and psychology. Although the illnesses are seldom discussed extensively, the philosophers were well aware of their existence and regarded their occurrence an indication of the soul s close dependence on the body. This called for a philosophical account. The second question addressed has to do with the ancient philosophers role as experts in mental problems of a non-medical kind, such as unwanted emotions. These problems were dubbed diseases of the soul , and the philosophers thus claimed to be doctors of the soul. Although the distinction between mental illnesses and diseases of the soul was often presented as rather obvious, there was some vagueness and overlap. There is still a third question that is explored, concerning the status of both mental illnesses and diseases of the soul as unnatural conditions, the role of the human body in the philosophical aetiologies of evil, and the medico-philosophical theories of psycho-physiological temperaments. This work consists of an introduction and five main chapters, focusing on Plato, Aristotle, the Stoics and Galen, and the Sceptics, the Epicureans and later Platonists. The sources drawn on are the original Greek and Latin philosophical and medical texts. It appears that the philosophers accepted the medical notion of mental illness, but interpreted it in various ways. The differences in interpretation were mostly attributable to differences in their theories of the soul. Although the distinction between mental illness and diseases of the soul was important, marking the boundary between the fields of expertise of medicine and philosophy, and of the individual s moral responsibilities, the problematic aspects of establishing it are discussed rather little in ancient philosophy. There may have been various reasons for this. The medical descriptions of mental illness are often extreme, symptoms of the psychotic type excluding the possibility of the condition being of the non-medical kind. In addition, the rigid normativeness of ancient philosophical anthropologies and their rigorous notion of human happiness decreased the need to assess the acceptability of individual variation in their emotional and intellectual lives and external behaviour.

Individuals on the Move : Body Condition Dependent Dispersal and Quasi-Local Competition in Metapopulations

Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

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.

Investigations of planetary boundary layer processes and particle formation in the atmosphere of planet Mars

The planet Mars is the Earth's neighbour in the Solar System. Planetary research stems from a fundamental need to explore our surroundings, typical for mankind. Manned missions to Mars are already being planned, and understanding the environment to which the astronauts would be exposed is of utmost importance for a successful mission. Information of the Martian environment given by models is already now used in designing the landers and orbiters sent to the red planet. In particular, studies of the Martian atmosphere are crucial for instrument design, entry, descent and landing system design, landing site selection, and aerobraking calculations. Research of planetary atmospheres can also contribute to atmospheric studies of the Earth via model testing and development of parameterizations: even after decades of modeling the Earth's atmosphere, we are still far from perfect weather predictions. On a global level, Mars has also been experiencing climate change. The aerosol effect is one of the largest unknowns in the present terrestrial climate change studies, and the role of aerosol particles in any climate is fundamental: studies of climate variations on another planet can help us better understand our own global change. In this thesis I have used an atmospheric column model for Mars to study the behaviour of the lowest layer of the atmosphere, the planetary boundary layer (PBL), and I have developed nucleation (particle formation) models for Martian conditions. The models were also coupled to study, for example, fog formation in the PBL. The PBL is perhaps the most significant part of the atmosphere for landers and humans, since we live in it and experience its state, for example, as gusty winds, nightfrost, and fogs. However, PBL modelling in weather prediction models is still a difficult task. Mars hosts a variety of cloud types, mainly composed of water ice particles, but also CO2 ice clouds form in the very cold polar night and at high altitudes elsewhere. Nucleation is the first step in particle formation, and always includes a phase transition. Cloud crystals on Mars form from vapour to ice on ubiquitous, suspended dust particles. Clouds on Mars have a small radiative effect in the present climate, but it may have been more important in the past. This thesis represents an attempt to model the Martian atmosphere at the smallest scales with high resolution. The models used and developed during the course of the research are useful tools for developing and testing parameterizations for larger-scale models all the way up to global climate models, since the small-scale models can describe processes that in the large-scale models are reduced to subgrid (not explicitly resolved) scale.

Coherent quasiparticle approximation cQPA and nonlocal coherence

We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum mechanical coherence evolution with a well defined collision integral giving rise to decoherence. Several applications of the method are given, for example to the coherent particle production, electroweak baryogenesis and study of decoherence and thermalization.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.