<p>Behaviour occurs in time, and precise timing in the range of seconds and fractions of seconds is for most living organisms necessary for successful interaction with the environment. Our ability to time discrete actions and to predict events on the basis of prior events indicates the existence of an internal timing mechanism. The nature of this mechanism provides essential constraints on models of the functional organisation of the brain. </p><p>The present work indicates that there are discontinuities in the function of time close to 1 s and 1.4 s, both in the amount of drift in a series of produced intervals (Study I) and in the detectability of drift in a series of sounds (Study II). The similarities across different tasks further suggest that action and perceptual judgements are governed by the same (kind of) mechanism. Study III showed that series of produced intervals could be characterised by different amounts of positive fractal dependency related to the aforementioned discontinuities. </p><p>In conjunction with other findings in the literature, these results suggest that timing of intervals up to a few seconds is strongly dependent on previous intervals and on the duration to be timed. This argues against a clock-counter mechanism, as proposed by scalar timing theory, according to which successive intervals are random and the size of the timing error conforms to Weber's law. </p><p>A functional model is proposed, expressed in an autoregressive framework, which consists of a single-interval timer with error corrective feedback. The duration-specificity of the proposed model is derived from the order of error correction, as determined by a semi-flexible temporal integration span. </p>

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

Behaviour occurs in time, and precise timing in the range of seconds and fractions of seconds is for most living organisms necessary for successful interaction with the environment. Our ability to time discrete actions and to predict events on the basis of prior events indicates the existence of an internal timing mechanism. The nature of this mechanism provides essential constraints on models of the functional organisation of the brain. The present work indicates that there are discontinuities in the function of time close to 1 s and 1.4 s, both in the amount of drift in a series of produced intervals (Study I) and in the detectability of drift in a series of sounds (Study II). The similarities across different tasks further suggest that action and perceptual judgements are governed by the same (kind of) mechanism. Study III showed that series of produced intervals could be characterised by different amounts of positive fractal dependency related to the aforementioned discontinuities. In conjunction with other findings in the literature, these results suggest that timing of intervals up to a few seconds is strongly dependent on previous intervals and on the duration to be timed. This argues against a clock-counter mechanism, as proposed by scalar timing theory, according to which successive intervals are random and the size of the timing error conforms to Weber's law. A functional model is proposed, expressed in an autoregressive framework, which consists of a single-interval timer with error corrective feedback. The duration-specificity of the proposed model is derived from the order of error correction, as determined by a semi-flexible temporal integration span.

An extended Förster theory (EFT), previously derived (L. B.-Å. Johansson et al. J. Chem. Phys., 1996,105) has theoretically been adapted and used in simulations of donor-acceptor energy transfer (DAET), which is a process often referred to as FRET. It was shown that the classical Förster theory is only valid in the initial part of the fluorescence decay. In this thesis an EFT is derived and outlined for electronic energy transport between two fluorescent molecules which are chemically identical, but photophysically non-identical. The energy migration within such asymmetric pairs is partially reversible and therefore referred to as partial donor-donor energy migration (PDDEM). The previously derived model of PDDEM (S. V. Kalinin et al. Spectrochim Acta Part A, 2002,58) is an approximation of the EFT. In particular, the EFT accounts for the time-dependent reorientations as well as the distance that influence the rate of electronic energy migration. The reorientation of the fluorophores transition dipole moments has been simulated using Brownian dynamics. As a result, the related “k2-problem” has been solved. The EFT of PDDEM has also been studied regarding the effect of PDDEM on experimental observables e.g. quantum yield of fluorescence and steady-state anisotropies

Micro- or nanometer sized magnetic particles (beads) currently have a vast range of life science applications in, for example, bioseparation techniques, cancer therapy, development of contrast agents and biosensing techniques. In the latter field, magnetic beads offer several unique advantages, including minimal background signals, physical and chemical stability and low manufacturing costs. Because of these properties, magnetic biosensing techniques are potential candidates for low-cost, easy-to-use molecular diagnostic devices. This doctoral thesis focuses mainly on the proof of principle and further development of a new magnetic biosensor platform for detection of DNA targets, a potential candidate for a new generation of low-cost, easy-to-use diagnostic devices: the Volume-Amplified Magnetic Nanobead Detection Assay (VAM-NDA). The VAM-NDA principle combines target recognition by padlock probe ligation followed by rolling circle amplification (RCA) of the reacted probes with changes in Brownian relaxation behaviour of magnetic nanobeads (typically ~100 nm in diameter) induced by a change in hydrodynamic bead volume. More specifically, the RCA products (coils, typically ~1 μm in diameter) are detected magnetically by adding magnetic beads tagged with detection probes complementary to part of the repeating RCA-coil sequence. Thus, depending on the target concentration, a certain quantity of beads binds to the coils by base-pair hybridisation (bead immobilisation), resulting in a dramatic bead volume increase, which is then detected by measuring the complex magnetisation spectrum. Use of a commercial SQUID magnetometer for measuring complex magnetisation resulted in a detection limit in the low pM range for DNA targets with excellent quantification accuracy. Simultaneous multiplexing was also evaluated. The stability and aging of typical commercial ferrofluids (suspensions of magnetic beads) were investigated by measuring the complex magnetisation of and interbead interactions in oligonucleotide-functionalised ferrofluids. In summary, the bead surface characteristics were found to have a strong impact on the measured dynamic magnetic properties.

Estimation of the self-similarity exponent has attracted growing interest in recent decades and became a research subject in various fields and disciplines. Real-world data exhibiting self-similar behavior and/or parametrized by self-similarity exponent (in particular Hurst exponent) have been collected in different fields ranging from finance and human sciencies to hydrologic and traffic networks. Such rich classes of possible applications obligates researchers to investigate qualitatively new methods for estimation of the self-similarity exponent as well as identification of long-range dependencies (or long memory). In this thesis I present the Bayesian estimation of the Hurst exponent. In contrast to previous methods, the Bayesian approach allows the possibility to calculate the point estimator and confidence intervals at the same time, bringing significant advantages in data-analysis as discussed in this thesis. Moreover, it is also applicable to short data and unevenly sampled data, thus broadening the range of systems where the estimation of the Hurst exponent is possible. Taking into account that one of the substantial classes of great interest in modeling is the class of Gaussian self-similar processes, this thesis considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed. / Die Abschätzung des Selbstähnlichkeitsexponenten hat in den letzten Jahr-zehnten an Aufmerksamkeit gewonnen und ist in vielen wissenschaftlichen Gebieten und Disziplinen zu einem intensiven Forschungsthema geworden. Reelle Daten, die selbsähnliches Verhalten zeigen und/oder durch den Selbstähnlichkeitsexponenten (insbesondere durch den Hurst-Exponenten) parametrisiert werden, wurden in verschiedenen Gebieten gesammelt, die von Finanzwissenschaften über Humanwissenschaften bis zu Netzwerken in der Hydrologie und dem Verkehr reichen. Diese reiche Anzahl an möglichen Anwendungen verlangt von Forschern, neue Methoden zu entwickeln, um den Selbstähnlichkeitsexponenten abzuschätzen, sowie großskalige Abhängigkeiten zu erkennen. In dieser Arbeit stelle ich die Bayessche Schätzung des Hurst-Exponenten vor. Im Unterschied zu früheren Methoden, erlaubt die Bayessche Herangehensweise die Berechnung von Punktschätzungen zusammen mit Konfidenzintervallen, was von bedeutendem Vorteil in der Datenanalyse ist, wie in der Arbeit diskutiert wird. Zudem ist diese Methode anwendbar auf kurze und unregelmäßig verteilte Datensätze, wodurch die Auswahl der möglichen Anwendung, wo der Hurst-Exponent geschätzt werden soll, stark erweitert wird. Unter Berücksichtigung der Tatsache, dass der Gauß'sche selbstähnliche Prozess von bedeutender Interesse in der Modellierung ist, werden in dieser Arbeit Realisierungen der Prozesse der fraktionalen Brown'schen Bewegung und des fraktionalen Gauß'schen Rauschens untersucht. Zusätzlich werden Anwendungen auf reelle Daten, wie Wasserstände des Nil und fixierte Augenbewegungen, diskutiert.

This thesis describes the results of experimental work on polyelectrolyte gels and their interaction with oppositely charged surfactants, and presents two new algorithms applicable to the simulation of colloid and polymer systems. The model systems investigated were crosslinked poly(acrylate) (PA) and poly(styrene sulphonate) (PSS), and the surfactant was dodecyl trimethylammonium bromide (DoTAB). Pure gel materials were studied using dynamic light scattering. It was shown that the diffusion coefficient (D) increases with increasing degree of swelling and the concentration dependence is larger than predicted by scaling arguments. For gels at swelling equilibrium D increases with increasing degree of crosslinking. In subsequent studies on gel particles in DoTAB solution, Raman spectra were recorded at different positions in the gel. For both types of gels two distinct regions could be observed. For PA the surfactant is localised in the outer phase without any surfactant in the core, while for PSS the surfactant was distributed such that it had the same concentration relative to the polymer throughout the gel. In a second experiment, the kinetics for the deswelling of microscopic PSS particles in DoTAB solution was studied. It was found that the final volume varied linearly with the DoTAB concentration, and the rate of volume decrease could be fitted to a single exponential indicating stagnant layer diffusion to be the rate limiting process for the deswelling of the PSS particles. In the second part, I first describe an algorithm showing an efficient way to detect percolation in simulations, with periodic boundary conditions, using recursion. Spherical boundary conditions is an alternative to periodic boundary conditions for systems with long-range interactions. In the last part, the possibility to use the surface of a hypersphere in four dimensions for simulations of polymer systems is investigated, and algorithms for Monte Carlo and Brownian dynamics simulations are described.

A stochastic differential equationdriven by a Brownian motion where the dispersion is determined by a parameter is considered. The parameter undergoes a change at a certain time point. Estimates of the time change point and the parameter, before and after that time, is considered.The estimates were presented in Lacus 2008. Two cases are considered: (1) the drift is known, (2) the drift is unknown and the dispersion space-independent. Applications to Dow-Jones index 1971-1974  and Goldmann-Sachs closings 2005-- May 2009 are given.

Recently there have been reports that certain physiological data seem to have the properties of long-range correlation and self-similarity. These two properties can be characterized by a long-range dependent parameter d, as well as a self-similar parameter H. In Peng et al (1995), the alteration of long-range correlations with life-threatening pathologies are studied by analyzing the heart rate data of different groups of subjects. The self-similarity properties of two well-known processes, namely the Fractional Brownian Motion (FBM) and the Fractional ARIMA (FARIMA), are of interest to see if it is suitable to be used to model the heart rate data in order to examine the health conditions of some patients. The Embedded Branching Process (EBP) method for estimating parameter $H$ and a goodness of fit test for examining the self-similarity of a process based on the EBP method are proposed in Jones and Shen (2004). In this work, the performance of the goodness of fit test are examined using simulated data from the FBM and FARIMA processes. A modification of the distribution of the test statistics under null hypothesis is proposed and has been modified to be more appropriate. Some simulation comparisons of different estimation methods of the parameter $H$ for some FARIMA processes are also presented and applied to heart rate data obtained from Kaohsiung Veterans General Hospital.

Dans cette thèse on étudie des schémas numériques pour des processus<br />/X/ à coefficients discontinus. Un premier schéma pour le cas<br />unidimensionnel utilise les Équations Différentielles Stochastiques<br />avec Temps Local. En effet en dimension un les processus /X/ sont<br />solutions de telles équations. On construit une grille sur la droite<br />réelle, qu'une bijection adéquate transforme en une grille uniforme<br />de pas /h/. Cette bijection permet de transformer /X/ en /Y/ qui se<br />comporte localement comme un Skew Brownian Motion, pour lequel on<br />connaît les probabilités de transition sur une grille uniforme, et le<br />temps moyen passé sur chaque cellule de cette grille. Une marche<br />aléatoire peut alors être construite, qui converge vers /X/ en racine<br />de /h/. Toujours dans le cas unidimensionnel on propose un deuxième<br />schéma plus général. On se donne une grille non uniforme sur la<br />droite réelle, dont les cellules ont une taille proportionnelle à<br />/h/. On montre qu'on peut relier les probabilités de transition de<br />/X/ sur cette grille, ainsi que le temps moyen passé par /X/ sur<br />chacune de ses cellules, à des solutions de problèmes d'EDP<br />elliptiques ad hoc. Une marche aléatoire en temps et en espace est<br />ainsi construite, qui permet d'approcher /X/ à nouveau en racine de<br />/h/. Ensuite on présente des pistes pour adapter cette dernière<br />approche au cas bidimensionnel et les problèmes que cela soulève.<br />Enfin on illustre par des exemples numériques les schémas étudiés.