Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

Becoming to Know: Essays on Extended Epistemology of Knowledge Creation

This qualitative, explorative study, which comprises four essays, focuses on knowledge management (KM). It seeks to answer the question: How can the knowledge creation theory of KM benefit from social learning theories? While studying the five development phases of knowledge creation theory of KM through 1995-2008 and applying some social learning theories in essays, the concepts of knowing, learning and becoming have emerged. Drawing on these three concepts and on becoming ontology and extended epistemology as research philosophies the study suggests the ‘becoming epistemology’ concept and develops the ‘becoming to know’ framework. The framework proposes becoming as phronesis of dialectic interactions between learning and knowing. It shows how becoming to know evolves as an interplay between concrete experience and logical thinking in the present and in a living context. The proposed framework could be considered a contribution to the current development phase of the knowledge creation theory of KM because it illustrates how ontological and epistemological knowledge spirals come together, which is the essence of the knowledge creation theory of KM.

Systems between information and knowledge : In a memory management model of an extended enterprise

The research question of this thesis was how knowledge can be managed with information systems. Information systems can support but not replace knowledge management. Systems can mainly store epistemic organisational knowledge included in content, and process data and information. Certain value can be achieved by adding communication technology to systems. All communication, however, can not be managed. A new layer between communication and manageable information was named as knowformation. Knowledge management literature was surveyed, together with information species from philosophy, physics, communication theory, and information system science. Positivism, post-positivism, and critical theory were studied, but knowformation in extended organisational memory seemed to be socially constructed. A memory management model of an extended enterprise (M3.exe) and knowformation concept were findings from iterative case studies, covering data, information and knowledge management systems. The cases varied from groups towards extended organisation. Systems were investigated, and administrators, users (knowledge workers) and managers interviewed. The model building required alternative sets of data, information and knowledge, instead of using the traditional pyramid. Also the explicit-tacit dichotomy was reconsidered. As human knowledge is the final aim of all data and information in the systems, the distinction between management of information vs. management of people was harmonised. Information systems were classified as the core of organisational memory. The content of the systems is in practice between communication and presentation. Firstly, the epistemic criterion of knowledge is not required neither in the knowledge management literature, nor from the content of the systems. Secondly, systems deal mostly with containers, and the knowledge management literature with applied knowledge. Also the construction of reality based on the system content and communication supports the knowformation concept. Knowformation belongs to memory management model of an extended enterprise (M3.exe) that is divided into horizontal and vertical key dimensions. Vertically, processes deal with content that can be managed, whereas communication can be supported, mainly by infrastructure. Horizontally, the right hand side of the model contains systems, and the left hand side content, which should be independent from each other. A strategy based on the model was defined.