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.

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.

Crystallization as a Tool for Controlling and Designing Properties of Pharmaceutical Solids

The ability to deliver the drug to the patient in a safe, efficacious and cost-effective manner depends largely on the physicochemical properties of the active pharmaceutical ingredient (API) in the solid state. In this context, crystallization is of critical importance in pharmaceutical industry, as it defines physical and powder properties of crystalline APIs. An improved knowledge of the various aspects of crystallization process is therefore needed. The overall goal of this thesis was to gain better understanding of the relationships between crystallization, solid-state form and properties of pharmaceutical solids with a focus on a crystal engineering approach to design technological properties of APIs. Specifically, solid-state properties of the crystalline forms of the model APIs, erythromycin A and baclofen, and the influence of solvent on their crystallization behavior were investigated. In addition, the physical phenomena associated with wet granulation and hot-melting processing of the model APIs were examined at the molecular level. Finally, the effect of crystal habit modification of a model API on its tabletting properties was evaluated. The thesis enabled the understanding of the relationship between the crystalline forms of the model APIs, which is of practical importance for solid-state control during processing and storage. Moreover, a new crystalline form, baclofen monohydrate, was discovered and characterized. Upon polymorph screening, erythromycin A demonstrated high solvate-forming propensity thus emphasizing the need for careful control of the solvent effects during formulation. The solvent compositions that yield the desirable crystalline form of erythromycin A were defined. Furthermore, new examples on solvent-mediated phase transformations taking place during wet granulation of baclofen and hot-melt processing of erythromycin A dihydrate with PEG 6000 are reported. Since solvent-mediated phase transformations involve the crystallization of a stable phase and hence affect the dissolution kinetics and possibly absorption of the API these transformations must be well documented. Finally, a controlled-crystallization method utilizing HPMC as a crystal habit modifier was developed for erythromycin A dihydrate. The crystals with modified habit were shown to posses improved compaction properties as compared with those of unmodified crystals. This result supports the idea of morphological crystal engineering as a tool for designing technological properties of APIs and is of utmost practical interest.

From Polymorph Screening to Dissolution Testing - Solid Phase Analysis during Pharmaceutical Development and Manufacturing

Solid materials can exist in different physical structures without a change in chemical composition. This phenomenon, known as polymorphism, has several implications on pharmaceutical development and manufacturing. Various solid forms of a drug can possess different physical and chemical properties, which may affect processing characteristics and stability, as well as the performance of a drug in the human body. Therefore, knowledge and control of the solid forms is fundamental to maintain safety and high quality of pharmaceuticals. During manufacture, harsh conditions can give rise to unexpected solid phase transformations and therefore change the behavior of the drug. Traditionally, pharmaceutical production has relied on time-consuming off-line analysis of production batches and finished products. This has led to poor understanding of processes and drug products. Therefore, new powerful methods that enable real time monitoring of pharmaceuticals during manufacturing processes are greatly needed. The aim of this thesis was to apply spectroscopic techniques to solid phase analysis within different stages of drug development and manufacturing, and thus, provide a molecular level insight into the behavior of active pharmaceutical ingredients (APIs) during processing. Applications to polymorph screening and different unit operations were developed and studied. A new approach to dissolution testing, which involves simultaneous measurement of drug concentration in the dissolution medium and in-situ solid phase analysis of the dissolving sample, was introduced and studied. Solid phase analysis was successfully performed during different stages, enabling a molecular level insight into the occurring phenomena. Near-infrared (NIR) spectroscopy was utilized in screening of polymorphs and processing-induced transformations (PITs). Polymorph screening was also studied with NIR and Raman spectroscopy in tandem. Quantitative solid phase analysis during fluidized bed drying was performed with in-line NIR and Raman spectroscopy and partial least squares (PLS) regression, and different dehydration mechanisms were studied using in-situ spectroscopy and partial least squares discriminant analysis (PLS-DA). In-situ solid phase analysis with Raman spectroscopy during dissolution testing enabled analysis of dissolution as a whole, and provided a scientific explanation for changes in the dissolution rate. It was concluded that the methods applied and studied provide better process understanding and knowledge of the drug products, and therefore, a way to achieve better quality.

Investigating physical properties of solid dosage forms during pharmaceutical processing : Process analytical applications of vibrational spectroscopy

In order to improve and continuously develop the quality of pharmaceutical products, the process analytical technology (PAT) framework has been adopted by the US Food and Drug Administration. One of the aims of PAT is to identify critical process parameters and their effect on the quality of the final product. Real time analysis of the process data enables better control of the processes to obtain a high quality product. The main purpose of this work was to monitor crucial pharmaceutical unit operations (from blending to coating) and to examine the effect of processing on solid-state transformations and physical properties. The tools used were near-infrared (NIR) and Raman spectroscopy combined with multivariate data analysis, as well as X-ray powder diffraction (XRPD) and terahertz pulsed imaging (TPI). To detect process-induced transformations in active pharmaceutical ingredients (APIs), samples were taken after blending, granulation, extrusion, spheronisation, and drying. These samples were monitored by XRPD, Raman, and NIR spectroscopy showing hydrate formation in the case of theophylline and nitrofurantoin. For erythromycin dihydrate formation of the isomorphic dehydrate was critical. Thus, the main focus was on the drying process. NIR spectroscopy was applied in-line during a fluid-bed drying process. Multivariate data analysis (principal component analysis) enabled detection of the dehydrate formation at temperatures above 45°C. Furthermore, a small-scale rotating plate device was tested to provide an insight into film coating. The process was monitored using NIR spectroscopy. A calibration model, using partial least squares regression, was set up and applied to data obtained by in-line NIR measurements of a coating drum process. The predicted coating thickness agreed with the measured coating thickness. For investigating the quality of film coatings TPI was used to create a 3-D image of a coated tablet. With this technique it was possible to determine coating layer thickness, distribution, reproducibility, and uniformity. In addition, it was possible to localise defects of either the coating or the tablet. It can be concluded from this work that the applied techniques increased the understanding of physico-chemical properties of drugs and drug products during and after processing. They additionally provided useful information to improve and verify the quality of pharmaceutical dosage forms

La modernización entre cafetales : San José, Costa Rica, 1880-1930

This work examines the urban modernization of San José, Costa Rica, between 1880 and 1930, using a cultural approach to trace the emergence of the bourgeois city in a small Central American capital, within the context of order and progress. As proposed by Henri Lefebvre, Manuel Castells and Edward Soja, space is given its rightful place as protagonist. The city, subject of this study, is explored as a seat of social power and as the embodiment of a cultural transformation that took shape in that space, a transformation spearheaded by the dominant social group, the Liberal elite. An analysis of the product built environment allows us to understand why the city grew in a determined manner: how the urban space became organized and how its infrastructure and services distributed. Although the emphasis is on the Liberal heyday from 1880-1930, this study also examines the history of the city since its origins in the late colonial period through its consolidation as a capital during the independent era, in order to characterize the nineteenth century colonial city that prevailed up to 1890 s. A diverse array of primary sources including official acts, memoirs, newspaper sources, maps and plans, photographs, and travelogues are used to study the initial phase of San Jose s urban growth. The investigation places the first period of modern urban growth at the turn of the nineteenth century within the prevailing ideological and political context of Positivism and Liberalism. The ideas of the city s elite regarding progress were translated into and reflected in the physical transformation of the city and in the social construction of space. Not only the transformations but also the limits and contradictions of the process of urban change are examined. At the same time, the reorganization of the city s physical space and the beginnings of the ensanche are studied. Hygiene as an engine of urban renovation is explored by studying the period s new public infrastructure (including pipelines, sewer systems, and the use of asphalt pavement) as part of the Saneamiento of San José. The modernization of public space is analyzed through a study of the first parks, boulevards and monuments and the emergence of a new urban culture prominently displayed in these green spaces. Parks and boulevards were new public and secular places of power within the modern city, used by the elite to display and educate the urban population into the new civic and secular traditions. The study goes on to explore the idealized image of the modern city through an analysis of European and North American travelogues and photography. The new esthetic of theatrical-spectacular representation of the modern city constructed a visual guide of how to understand and come to know the city. A partial and selective image of generalized urban change presented only the bourgeois facade and excluded everything that challenged the idea of progress. The enduring patterns of spatial and symbolic exclusion built into Costa Rica s capital city at the dawn of the twentieth century shed important light on the long-term political social and cultural processes that have created the troubled urban landscapes of contemporary Latin America.

Luce Irigaray's Philosophy of Feminine Being : Body, Desire and Wisdom

Luce Irigaray is a Belgian-born philosopher, psychoanalyst and linguist. Irigaray s concept of woman is crucial for understanding her own work but also for examining and developing the theoretical and methodological basis of feminist theory. This thesis argues that, ultimately, Irigaray s exploration of woman s being challenges our traditional notion of philosophy as a neutral discourse and the traditional notion of ourselves as philosophizing persons or human beings. However, despite its crucial role, Irigaray s idea of woman still lacks a comprehensive explication. This is because the discourse of sexual difference is blurred by the ideas of essentialism and biologism. --- Irigaray s concept of woman has been interpreted and criticized from the perspectives of metaphysical essentialism, strategic essentialism, realist essentialism and deconstructionism. This thesis argues that a reinterpretation is necessary to account for Irigaray s claims about the the traditional woman , mimesis, the specificity of the feminine body, feminine expression and sexual difference. Moreover, any reading should account for the differences between women and avoid giving a prescriptive function to the essence of woman. --- My thesis develops a new interpretation of Irigaray s concept of woman on the basis of the phenomenology of the body. It argues that Irigaray s discourse on woman can and must be understood by an idea of existential style. Existential style is embodied, affective and spiritual and it is constituted in relation to oneself, to others and to the world. It is temporal, it evolves and changes but preserves its open unity in its transformations. Stylistic unities, such as femininity or philosophy, are constituted in and by the singulars. -- This study discusses and analyses feminine existential style as a central theme and topic of Irigaray s works and shows how her work operates as a primary and paradigmatic example of the feminine style. These tasks are performed by studying the mimetic positions available for women and by explicating the phenomenological background of Irigaray s conceptions of the philosophical method, and the lived, expressive and affective body. The critical occupation and transformation of these mimetic positions, the inquiry into the first-person pre-discursive experience, and the cultivation of feminine expressivity open up the possibility of becoming a woman writer, a woman lover and a woman philosopher. The appearance of these new feminine figures is a precondition for the realization of sexual difference. So Irigaray opens up the possibility of sexual difference by instituting and constituting a feminine subject of love and wisdom, and by problematizing the idea of a neutral and absolute subject.

Om naturens förvandlingar : Vetenskap, kunskap och frihet i Rudolf Steiners tidiga tänkande. Idéhistoriska perspektiv på Waldorfpedagogiken

TRANSFORMATIONS OF NATURE Science, Knowledge and Freedom in the Early Thinking of Rudolf Steiner. Perspectives on Waldorf Education in the light of the History of Ideas Waldorf Education is based on the worldview that Rudolf Steiner (1861-1925) developed to a wide-ranging anthroposophical movement in the first decades of the 20th century. This thesis takes as its departure the early thinking of Rudolf Steiner that precedes anthroposophy, and its main purpose is to uncover the tradition of ideas represented in Steiner´s early life and which, in different ways, have emerged in the practice of Waldorf Education. Through systematic analysis I attempt to bring to light different aspects of Steiner’s early thinking: his concept of science, his epistemological startingpoints and his philosophy of freedom. By departing from J. W. Goethe’s qualitative concept of science, Steiner strove in his early works to formulate a monistic worldview which appears to be closely related to the Romantic Movement and its philosophy of nature. Characteristic traits of his thinking are, on the one hand, a critique of a one-sided enlightenment and, on the other hand, an aspiration to see the world as a living organic unity. Human beings can, by developing our intuitive faculties, get a deeper understanding of the indissoluble relationship between man and nature. Against this background Steiner´s early thinking can be read as a special kind of romantic development narrative. Steiner’s early thinking also opens the way for romantic perspectives on Waldorf Education. It appears that many central aims and conceptions in Waldorf Education can be illuminated by the epistemological perspective upon which Steiner elaborated early in his life. An organic curriculum, phenomenological didactics and high ideal of freedom can be considered seen as educational applications of conceptions that played an important role in Goethe and his age. Thus, Waldorf Education provides in our contemporary society an exceptional set of educational values: a holistic education with romantic undertones.

Kaveriporukasta liiketoiminnaksi : Tuotannon häiriöt ja organisaation oppiminen nopeasti muuttuvassa yrityksessä

In the 1990 s the companies utilizing and producing new information technology, especially so-called new media, were also expected to be forerunners in new forms of work and organization. Researchers anticipated that new, more creative forms of work and the changing content of working life were about to replace old industrial and standardized ways of working. However, research on actual companies in the IT sector revealed a situation where only minor changes to existing organizational forms were seen .Many of the independent companies faced great difficulties trying to survive the rapid changes in the products and production forms in the emerging field. Most of the research on the new media field has been conducted as surveys, and an understanding of the actual everyday work process has remained thin. My research is a longitudinal study of the early phases of one new media company in Finland. The study is an analysis of the challenges the company faced in a rapidly changing business field and the attempts to overcome these challenges. The two main analyses in the study focus on the developmental phases of the company and the disturbances in the production process. Based on these analyses, I study changes and learning at work using the methodological framework of developmental work research. Developmental work research is a Finnish variant of the cultural-historical activity theory applied to the study of learning and transformations at work. The data was gathered over a three-year period of ethnographic fieldwork. I documented the production processes and everyday life in the company as a participant observer. I interviewed key persons, video and audio-taped meetings, followed e-mail correspondence and collected various documents, such as agreements and memos. I developed a systematic method for analyzing the disturbances in the production process by combining the various data sources. The systematic analysis of the disturbances depicted a very complex and only partly managed production process. The production process had a long duration, and no single actor had an understanding of it as a whole. Most of the disturbances had to do with the customer relationships. The nature of the disturbances was latent; they were recognized but not addressed. In the particular production processes that I analyzed, the ending life span of a particular product, a CD-ROM, became obvious. This finding can be interpreted in relation to the developmental phase of the production and the transformation of the field as a whole. Based on the analysis of the developmental phases and the disturbances, I formulate a hypothesis of the contradictions and developmental potentials of the activity studied. The conclusions of the study challenge the existing understanding of how to conceptualize and study organizational learning in production work. Most theories of organizational learning do not address qualitative changes in production nor historical challenges of organizational learning itself. My study opens up a new horizon in understanding organizational learning in a rapidly changing field where a learning culture based on craft or mass production work is insufficient. There is a need for anticipatory and proactive organizational learning. Proactive learning is needed to anticipate the changes in production type, and the life cycles of products.

Suhteessa kohteeseen ja suhteessa toisiin : Oppiminen ja vuorovaikutus opettajaopiskelijoiden suunnittelutapaamisessa

Objectives. In this research I analyzed the learning process of teacher students in a planning meeting using the expansive learning cycle and types of interaction approaches. In activity theory framework the expansive learning cycle has been applied widely in analyzing learning processes taking several years. However, few studies exist utilizing expansive cycles in analyzing short single meetings. In the activity theory framework talk and interaction have been analyzed using following types of interaction: coordination, cooperation and communication. In these studies single interaction situations have been analyzed, in which the status and power positions of participants has been very different. Interactions of self-directed teams, in which the participants are equal, have been examined very little. I am not aware of any studies, in which both learning actions of the expansive cycle and types of interaction by analyzing the same data would have been utilized. The aim of my study was to describe the process of collaborative innovative learning in a situation where the student group tries to accomplish a broad and ill-defined learning task. I aim to describe, how this planning process proceeds through different phases of learning actions of the expansive cycle. My goal is to understand and describe the transformations in the quality of interaction and transitions which are related to it. Another goal of this study is to specify the possible similarities and differences between expansive learning and types of interactions. Methods. Data of this study consisted of videotaped meetings, which were part of the study module for class teacher degree. The first meeting of the study module was chosen to be the primary research material. Five students were present in the group meeting. Transcription of the conversation was analyzed by classifying the turns of conversation following phases of the expansive cycle. After that the material was categorized again by using types of interaction. Results and conclusions. As a result of this study I was able to trace all the phases of the expansive cycle except one. Also, I was able to identify all interaction types. When I compared the two modes of analysis side by side I was able to find connecting main phases. Thus I was able to identify the interdependence between the two ways of analysis on a higher level, although I was not able to notice correlation on the level of individual phases. Based on this, I conclude that learning of the group was simultaneously specification and formulation of the object at the different phases of expansive learning and transformation of the quality of the interaction while searching for the common object.

Plant secondary compounds and soil microbial processes in carbon and nitrogen cycling in relation to tree species

The aim of this study was to explore soil microbial activities related to C and N cycling and the occurrence and concentrations of two important groups of plant secondary compounds, terpenes and phenolic compounds, under silver birch (Betula pendula Roth), Norway spruce (Picea abies (L.) Karst) and Scots pine (Pinus sylvestris L.) as well as to study the effects of volatile monoterpenes and tannins on soil microbial activities. The study site, located in Kivalo, northern Finland, included ca. 70-year-old adjacent stands dominated by silver birch, Norway spruce and Scots pine. Originally the soil was very probably similar in all three stands. All forest floor layers (litter (L), fermentation layer (F) and humified layer (H)) under birch and spruce showed higher rates of CO2 production, greater net mineralisation of nitrogen and higher amounts of carbon and nitrogen in microbial biomass than did the forest floor layers under pine. Concentrations of mono-, sesqui-, di- and triterpenes were higher under both conifers than under birch, while the concentration of total water-soluble phenolic compounds as well as the concentration of condensed tannins tended to be higher or at least as high under spruce as under birch or pine. In general, differences between tree species in soil microbial activities and in concentrations of secondary compounds were smaller in the H layer than in the upper layers. The rate of CO2 production and the amount of carbon in the microbial biomass correlated highly positively with the concentration of total water-soluble phenolic compounds and positively with the concentration of condensed tannins. Exposure of soil to volatile monoterpenes and tannins extracted and fractionated from spruce and pine needles affected carbon and nitrogen transformations in soil, but the effects were dependent on the compound and its molecular structure. Monoterpenes decreased net mineralisation of nitrogen and probably had a toxic effect on part of the microbial population in soil, while another part of the microbes seemed to be able to use monoterpenes as a carbon source. With tannins, low-molecular-weight compounds (also compounds other than tannins) increased soil CO2 production and nitrogen immobilisation by soil microbes while the higher-molecular-weight condensed tannins had inhibitory effects. In conclusion, plant secondary compounds may have a great potential in regulation of C and N transformations in forest soils, but the real magnitude of their significance in soil processes is impossible to estimate.

Noncommutative Gravitation as a Gauge Theory of Twisted Poincaré Symmetry

Gravitaation kvanttiteorian muotoilu on ollut teoreettisten fyysikkojen tavoitteena kvanttimekaniikan synnystä lähtien. Kvanttimekaniikan soveltaminen korkean energian ilmiöihin yleisen suhteellisuusteorian viitekehyksessä johtaa aika-avaruuden koordinaattien operatiiviseen ei-kommutoivuuteen. Ei-kommutoivia aika-avaruuden geometrioita tavataan myös avointen säikeiden säieteorioiden tietyillä matalan energian rajoilla. Ei-kommutoivan aika-avaruuden gravitaatioteoria voisi olla yhteensopiva kvanttimekaniikan kanssa ja se voisi mahdollistaa erittäin lyhyiden etäisyyksien ja korkeiden energioiden prosessien ei-lokaaliksi uskotun fysiikan kuvauksen, sekä tuottaa yleisen suhteellisuusteorian kanssa yhtenevän teorian pitkillä etäisyyksillä. Tässä työssä tarkastelen gravitaatiota Poincarén symmetrian mittakenttäteoriana ja pyrin yleistämään tämän näkemyksen ei-kommutoiviin aika-avaruuksiin. Ensin esittelen Poincarén symmetrian keskeisen roolin relativistisessa fysiikassa ja sen kuinka klassinen gravitaatioteoria johdetaan Poincarén symmetrian mittakenttäteoriana kommutoivassa aika-avaruudessa. Jatkan esittelemällä ei-kommutoivan aika-avaruuden ja kvanttikenttäteorian muotoilun ei-kommutoivassa aika-avaruudessa. Mittasymmetrioiden lokaalin luonteen vuoksi tarkastelen huolellisesti mittakenttäteorioiden muotoilua ei-kommutoivassa aika-avaruudessa. Erityistä huomiota kiinnitetään näiden teorioiden vääristyneeseen Poincarén symmetriaan, joka on ei-kommutoivan aika-avaruuden omaama uudentyyppinen kvanttisymmetria. Seuraavaksi tarkastelen ei-kommutoivan gravitaatioteorian muotoilun ongelmia ja niihin kirjallisuudessa esitettyjä ratkaisuehdotuksia. Selitän kuinka kaikissa tähänastisissa lähestymistavoissa epäonnistutaan muotoilla kovarianssi yleisten koordinaattimunnosten suhteen, joka on yleisen suhteellisuusteorian kulmakivi. Lopuksi tutkin mahdollisuutta yleistää vääristynyt Poincarén symmetria lokaaliksi mittasymmetriaksi --- gravitaation ei-kommutoivan mittakenttäteorian saavuttamisen toivossa. Osoitan, että tällaista yleistystä ei voida saavuttaa vääristämällä Poincarén symmetriaa kovariantilla twist-elementillä. Näin ollen ei-kommutoivan gravitaation ja vääristyneen Poincarén symmetrian tutkimuksessa tulee jatkossa keskittyä muihin lähestymistapoihin.