Understanding solid-state transformations during dehydration: new insights using vibrational spectroscopy and multivariate modelling

Many active pharmaceutical ingredients (APIs) have both anhydrate and hydrate forms. Due to the different physicochemical properties of solid forms, the changes in solid-state may result in therapeutic, pharmaceutical, legal and commercial problems. In order to obtain good solid dosage form quality and performance, there is a constant need to understand and control these phase transitions during manufacturing and storage. Thus it is important to detect and also quantify the possible transitions between the different forms. In recent years, vibrational spectroscopy has become an increasingly popular tool to characterise the solid-state forms and their phase transitions. It offers several advantages over other characterisation techniques including an ability to obtain molecular level information, minimal sample preparation, and the possibility of monitoring changes non-destructively in-line. Dehydration is the phase transition of hydrates which is frequently encountered during the dosage form production and storage. The aim of the present thesis was to investigate the dehydration behaviour of diverse pharmaceutical hydrates by near infrared (NIR), Raman and terahertz pulsed spectroscopic (TPS) monitoring together with multivariate data analysis. The goal was to reveal new perspectives for investigation of the dehydration at the molecular level. Solid-state transformations were monitored during dehydration of diverse hydrates on hot-stage. The results obtained from qualitative experiments were used to develop a method and perform the quantification of the solid-state forms during process induced dehydration in a fluidised bed dryer. Both in situ and in-line process monitoring and quantification was performed. This thesis demonstrated the utility of vibrational spectroscopy techniques and multivariate modelling to monitor and investigate dehydration behaviour in situ and during fluidised bed drying. All three spectroscopic methods proved complementary in the study of dehydration. NIR spectroscopy models could quantify the solid-state forms in the binary system, but were unable to quantify all the forms in the quaternary system. Raman spectroscopy models on the other hand could quantify all four solid-state forms that appeared upon isothermal dehydration. The speed of spectroscopic methods makes them applicable for monitoring dehydration and the quantification of multiple forms was performed during phase transition. Thus the solid-state structure information at the molecular level was directly obtained. TPS detected the intermolecular phonon modes and Raman spectroscopy detected mostly the changes in intramolecular vibrations. Both techniques revealed information about the crystal structure changes. NIR spectroscopy, on the other hand was more sensitive to water content and hydrogen bonding environment of water molecules. This study provides a basis for real time process monitoring using vibrational spectroscopy during pharmaceutical manufacturing.

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.

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Using Mathematical Morphology for Geometric Music Retrieval

The usual task in music information retrieval (MIR) is to find occurrences of a monophonic query pattern within a music database, which can contain both monophonic and polyphonic content. The so-called query-by-humming systems are a famous instance of content-based MIR. In such a system, the user's hummed query is converted into symbolic form to perform search operations in a similarly encoded database. The symbolic representation (e.g., textual, MIDI or vector data) is typically a quantized and simplified version of the sampled audio data, yielding to faster search algorithms and space requirements that can be met in real-life situations. In this thesis, we investigate geometric approaches to MIR. We first study some musicological properties often needed in MIR algorithms, and then give a literature review on traditional (e.g., string-matching-based) MIR algorithms and novel techniques based on geometry. We also introduce some concepts from digital image processing, namely the mathematical morphology, which we will use to develop and implement four algorithms for geometric music retrieval. The symbolic representation in the case of our algorithms is a binary 2-D image. We use various morphological pre- and post-processing operations on the query and the database images to perform template matching / pattern recognition for the images. The algorithms are basically extensions to classic image correlation and hit-or-miss transformation techniques used widely in template matching applications. They aim to be a future extension to the retrieval engine of C-BRAHMS, which is a research project of the Department of Computer Science at University of Helsinki.

Profligate Descent : The Cultural Transformations of Evolutionary Narrative

This dissertation traces a set of historical transformations the Darwinian evolutionary narrative has undergone toward the end of the twentieth century, especially as reflected in Anglo-American popular science books and novels. The study has three objectives. First, it seeks to understand the organizing logic of evolutionary narratives and the role that assumptions about gender and sexuality play in that logic. Second, it asks what kinds of cultural anxieties evolutionary theory raises and how evolutionary narratives negotiate them. Third, it examines the possibilities and limits of narrative transformation both as a historical phenomenon and as a theoretical question. This interdisciplinary dissertation is situated at the intersection of science studies, cultural studies, literary studies, and gender studies. Its understanding of science as a cultural practice that both emerges from and contributes to cultural expectations and institutional structures follows the tradition of science studies. Its focus on the question of popular appeal and the mechanisms of cultural change arises from cultural studies. Its view of narrative as a structural phenomenon is grounded in literary studies in general and feminist narrative theory in particular. Its understanding of gender and sexuality as implicated in discourses of epistemic authority builds on the view of gender and sexuality as contingent cultural categories central to gender studies. The primary material consists of over 25 British and American popular science books and novels, published roughly between 1990 and 2005. In order to highlight historical transformations, these texts are read in the context of Darwin s The Origin of Species and The Descent of Man, on the one hand, and such sociobiological classics as E. O. Wilson s On Human Nature and Richard Dawkins s The Selfish Gene, on the other. The research method combines feminist narrative analysis with cultural and historical contextualization, emphasizing discursive abruptions, recurrent narrative patterns, and underlying continuities. The dissertation demonstrates that the relationship between Darwin s evolutionary narrative and late twentieth-century evolutionary narratives is characterized by reemphasis, omissions, and continuous rewriting. In particular, contemporary evolutionary discourse extends the role assigned to reproduction both sexual and narrative in Darwin s writing, generating a narrative logic that imagines the desire to reproduce as the driving force of evolution and posits the reproductive sex act as the endlessly repeated narrative event that keeps the story going. The study argues that the popular appeal of evolutionary accounts of gender, sexuality, and human nature may arise, to an extent, from this reproductive narrative dynamic. This narrative dynamic, however, is not logically invulnerable. Since the continuation of the evolutionary narrative relies on successful reproduction, the possibility of reproductive failure poses a constant risk to narrative futurity, arousing cultural anxieties that evolutionary narratives need to address. The study argues that evolutionary narratives appease such anxieties by evoking a range of cultural narratives, especially romantic, religious, and national narratives. Furthermore, the study shows that the event-based logic of evolutionary narratives privileges observable acts over emotions, pleasures, identities, and desires, thus engendering a set of conceptual exclusions that limits the imaginative scope of evolution as a cultural narrative.

Mathematical modelling of groundwater pollution in a small heterogeneous aquifer at Kärkölä, southern Finland

Yhteenveto: Kärkölän likaantuneen pohjavesialueen matemaattinen mallinnus