30 resultados para mathematical understanding

em Helda - Digital Repository of University of Helsinki


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There is a need for better understanding of the processes and new ideas to develop traditional pharmaceutical powder manufacturing procedures. Process analytical technology (PAT) has been developed to improve understanding of the processes and establish methods to monitor and control processes. The interest is in maintaining and even improving the whole manufacturing process and the final products at real-time. Process understanding can be a foundation for innovation and continuous improvement in pharmaceutical development and manufacturing. New methods are craved for to increase the quality and safety of the final products faster and more efficiently than ever before. The real-time process monitoring demands tools, which enable fast and noninvasive measurements with sufficient accuracy. Traditional quality control methods have been laborious and time consuming and they are performed off line i.e. the analysis has been removed from process area. Vibrational spectroscopic methods are responding this challenge and their utilisation have increased a lot during the past few years. In addition, other methods such as colour analysis can be utilised in noninvasive real-time process monitoring. In this study three pharmaceutical processes were investigated: drying, mixing and tabletting. In addition tablet properties were evaluated. Real-time monitoring was performed with NIR and Raman spectroscopies, colour analysis, particle size analysis and compression data during tabletting was evaluated using mathematical modelling. These methods were suitable for real-time monitoring of pharmaceutical unit operations and increase the knowledge of the critical parameters in the processes and the phenomena occurring during operations. They can improve our process understanding and therefore, finally, enhance the quality of final products.

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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.

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The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

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From Arithmetic to Algebra. Changes in the skills in comprehensive school over 20 years. In recent decades we have emphasized the understanding of calculation in mathematics teaching. Many studies have found that better understanding helps to apply skills in new conditions and that the ability to think on an abstract level increases the transfer to new contexts. In my research I take into consideration competence as a matrix where content is in a horizontal line and levels of thinking are in a vertical line. The know-how is intellectual and strategic flexibility and understanding. The resources and limitations of memory have their effects on learning in different ways in different phases. Therefore both flexible conceptual thinking and automatization must be considered in learning. The research questions that I examine are what kind of changes have occurred in mathematical skills in comprehensive school over the last 20 years and what kind of conceptual thinking is demonstrated by students in this decade. The study consists of two parts. The first part is a statistical analysis of the mathematical skills and their changes over the last 20 years in comprehensive school. In the test the pupils did not use calculators. The second part is a qualitative analysis of the conceptual thinking of pupils in comprehensive school in this decade. The study shows significant differences in algebra and in some parts of arithmetic. The largest differences were detected in the calculation skills of fractions. In the 1980s two out of three pupils were able to complete tasks with fractions, but in the 2000s only one out of three pupils were able to do the same tasks. Also remarkable is that out of the students who could complete the tasks with fractions, only one out of three pupils was on the conceptual level in his/her thinking. This means that about 10% of pupils are able to understand the algebraic expression, which has the same isomorphic structure as the arithmetical expression. This finding is important because the ability to think innovatively is created when learning the basic concepts. Keywords: arithmetic, algebra, competence

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Suusyöpä Teheranissa, Iranissa 1993-2003 Tämän väitöskirjan tavoitteena oli kuvata suusyövän yleisyyttä ja siihen vaikuttavia tekijöitä Teheranissa, Iranissa tutkimalla suusyöpäpotilaita, suusyöpäkasvainten ominaisuuksia, potilaille tehtyjä diagnooseja ja niiden viivästymistä sekä heidän selviytymistä sairaudestaan. Suusyöpäkasvainten tietoja kerättiin 1042 suusyöpäpotilaalta. Nämä tiedot kerättiin 30 suurimman Teheranilaissairaalan potilaskortistoista vuosien 1993-2003 ajalta. Eloonjäämisanalyysiä varten tiedot kerättiin vuosien 1996-2003 arkistoista 470 suusyöpä- ja 82 huulisyöpäpotilaan osalta ja heitä seurattiin vuoden 2005 loppuun. Potilaan kokemien ensioireiden ja lopullisen syöpädiagnoosin välistä viivettä varten kerättiin tiedot Teheranilaisista sairaaloista 100 peräkkäisen suusyöpäpotilaan tiedoista vuosien 2004-2006 välillä. Ns diagnostinen viive jaettiin kahteen osaan: 1) ensioireiden ja ensimmäisen sitä seuranneen lääkärikäynnin väli ja 2) ensimmäisen lääkärikäynnin ja lopullisen diagnoosin välinen ero. Useimmat suusyövät olivat pitkälle edenneitä diagnoosin tekemisen hetkellä, kasvain oli siis yli 4 senttimetriä halkaisijaltaan ja/tai kaulan alueen imusolmukkeissa oli jo etäpesäkkeitä. Eloonjäämistodennäköisyys viiden vuoden aikavälillä oli suusyöpäpotilaille 30% ja huulisyöpäpotilaille 62%, mitkä olivat merkittävästi alempia kuin yleisesti länsimaissa vastaavat luvut. Tämä tutkimus osoitti, että keskimääräinen diagnostinen viive oli korkea (7,2 kk, SD 7,5), erityisesti kun niitä verrataan kehittyneimpien terveydenhuoltojärjestelmien vastaaviin tietoihin. Yleensä potilaasta aiheutuva viive oli huomattavan suuri ensioireiden ja lopullisen diagnoosin välisestä ajasta. Tässä tutkimuksessa tehtyjen havaintojen pohjalta on perusteltua esittää kehitettäväksi ennaltaehkäisevä tiedotusohjelma, jossa kansalaiset voisivat saada enemmän tietoa suusyövästä, sen ensioireista jotta he hakeutuisivat aikaisemmin hoitoon. Lisäksi terveydenhoitohenkilöstöä, erityisesti hammaslääkärejä ja suuhygienistejä tulisi kouluttaa varhaisen diagnoosin tekemiseksi, jotta Iranissa tehtävien suusyöpähoitojen lopputulokset paranisivat.

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The sustainability of food production has increasingly attracted the attention of consumers, farmers, food and retailing companies, and politicians. One manifestation of such attention is the growing interest in organic foods. Organic agriculture has the potential to enhance the ecological modernisation of food production by implementing the organic method as a preventative innovation that simultaneously produces environmental and economic benefits. However, in addition to the challenges to organic farming, the small market share of organic products in many countries today and Finland in particular risks undermining the achievement of such benefits. The problems identified as hindrances to the increased consumption of organic food are the poor availability, limited variety and high prices of organic products, the complicated buying decisions and the difficulties in delivering the intangible value of organic foods. Small volumes and sporadic markets, high costs, lack of market information, as well as poor supply reliability are obstacles to increasing the volume of organic production and processing. These problems shift the focus from a single actor to the entire supply chain and require solutions that involve more interaction among the actors within the organic chain. As an entity, the organic food chain has received very little scholarly attention. Researchers have mainly approached the organic chain from the perspective of a single actor, or they have described its structure rather than the interaction between the actors. Consequently, interaction among the primary actors in organic chains, i.e. farmers, manufacturers, retailers and consumers, has largely gone unexamined. The purpose of this study is to shed light on the interaction of the primary actors within a whole organic chain in relation to the ecological modernisation of food production. This information is organised into a conceptual framework to help illuminate this complex field. This thesis integrates the theories and concepts of three approaches: food system studies, supply chain management and ecological modernisation. Through a case study, a conceptual system framework will be developed and applied to a real life-situation. The thesis is supported by research published in four articles. All examine the same organic chains through case studies, but each approaches the problem from a different, complementary perspective. The findings indicated that regardless of the coherent values emphasising responsibility, the organic chains were loosely integrated to operate as a system. The focus was on product flow, leaving other aspects of value creation largely aside. Communication with consumers was rare, and none of the actors had taken a leading role in enhancing the market for organic products. Such a situation presents unsuitable conditions for ecological modernisation of food production through organic food and calls for contributions from stakeholders other than those directly involved in the product chain. The findings inspired a revision of the original conceptual framework. The revised framework, the three-layer framework , distinguishes the different layers of interaction. By gradually enlarging the chain orientation the different but interrelated layers become visible. A framework is thus provided for further research and for understanding practical implications of the performance of organic food chains. The revised framework provides both an ideal model for organic chains in relation to ecological modernisation and demonstrates a situation consistent with the empirical evidence.

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Our present-day understanding of fundamental constituents of matter and their interactions is based on the Standard Model of particle physics, which relies on quantum gauge field theories. On the other hand, the large scale dynamical behaviour of spacetime is understood via the general theory of relativity of Einstein. The merging of these two complementary aspects of nature, quantum and gravity, is one of the greatest goals of modern fundamental physics, the achievement of which would help us understand the short-distance structure of spacetime, thus shedding light on the events in the singular states of general relativity, such as black holes and the Big Bang, where our current models of nature break down. The formulation of quantum field theories in noncommutative spacetime is an attempt to realize the idea of nonlocality at short distances, which our present understanding of these different aspects of Nature suggests, and consequently to find testable hints of the underlying quantum behaviour of spacetime. The formulation of noncommutative theories encounters various unprecedented problems, which derive from their peculiar inherent nonlocality. Arguably the most serious of these is the so-called UV/IR mixing, which makes the derivation of observable predictions especially hard by causing new tedious divergencies, to which our previous well-developed renormalization methods for quantum field theories do not apply. In the thesis I review the basic mathematical concepts of noncommutative spacetime, different formulations of quantum field theories in the context, and the theoretical understanding of UV/IR mixing. In particular, I put forward new results to be published, which show that also the theory of quantum electrodynamics in noncommutative spacetime defined via Seiberg-Witten map suffers from UV/IR mixing. Finally, I review some of the most promising ways to overcome the problem. The final solution remains a challenge for the future.

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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.

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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.

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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.

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The study investigated variation in the ways in which a group of students and teachers of Evangelical Lutheran religious education in Finnish upper secondary schools understand Lutheranism and searched for educational implications for learning in religious education. The aim of understanding the qualitative variation in understanding Lutheranism was explored through the relationship between the following questions, which correspond to the results reported in the following original refereed publications: 1) How do Finnish students understand Lutheranism? 2) How do Finnish teachers of religious education constitute the meaning of Lutheranism? 3) How could phenomenography and the Variation Theory of Learning contribute to learning about and from religion in the context of Finnish Lutheran Religious Education as compared to religious education in the UK? Two empirical studies (Hella, 2007; Hella, 2008) were undertaken from a phenomenographic research perspective (e.g., Marton, 1981) and the Variation Theory of Learning (e.g., Marton & Tsui et al. 2004) that developed from it. Data was collected from 63 upper secondary students and 40 teachers of religious education through written tasks with open questions and complementary interviews with 11 students and 20 teachers for clarification of meanings. The two studies focused on the content and structure of meaning discernment in students and teachers expressed understandings of Lutheranism. Differences in understandings are due to differences in the meanings that are discerned and focused on. The key differences between the ways students understand varied from understanding Lutheranism as a religion to personal faith with its core in mercy. The logical relationships between the categories that describe variation in understanding express a hierarchy of ascending complexity, according to which more developed understandings are inclusive of less developed ones. The ways the teachers understand relate to student s understandings in a sequential manner. Phenomenography and Variation Theory were discussed in the context of religious education in Finland and the UK in relation to the theoretical notion of learning about and from religion (Hella & Wright, 2008). The thesis suggests that variation theory enables religious educators to recognise the unity of learning about and from religion, as learning is always learning about something and involves simultaneous engagement with the object of learning and development as a person. The study also suggests that phenomenography and variation theory offer a means by which it is possible for academics, policy makers, curriculum designers, teachers and students to learn to discern different ways of understanding the contested nature of religions. Keywords: Lutheranism, understanding, variation, teaching, learning, phenomenography, religious education

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The aim of this study has been to discern what Manas Buthelezi (1935-), a black South African Lutheran theologian and later also a bishop, regards as the requirements a church has to fulfill in order to be credible in the apartheid society. Buthelezi’s dissertation and several articles written between the years 1968 and 1993 are the sources of this study. Also the lectures held in Heidelberg in 1972 are referred to. Systematic analysis is the method used. The question of the credibility of the church is studied through three concepts that play an important role in Buthelezi’s ecclesiological thought, namely the wholeness of life, incarnation and liberation. The notion of the wholeness of life stems from the African tradition. Buthelezi takes the concept into the Christian church: the church should realize that God is the Creator of all life and Christ the lord of every aspect of human existence. Life is one entity coram Deo. However, the church is not to become the world; solidarity between the two must remain critical as the church is also called to play a prophetic role in the society. The church is in an open relationship with the world. It has a unique message of forgiveness and reconciliation. Nevertheless, the message is not a possession of the church but it is addressed to the whole world. The meaning of incarnation comes close to that of the wholeness of life. Following the example of Christ’s incarnation, the church must become human in the reality of the people. The church in Soweto is to become the people of Soweto, that is, the church must become as vulnerable as the people are. An incarnate church cannot be immune to the oppression that people experience, because the people are the church. The church is therefore bound to suffer. Buthelezi’s theology of the cross is pragmatic: the suffering of the church aims at the liberation of the oppressed. At times the physical presence of the church by the side of the suffering people is the only way to preach the incarnate gospel. In the South Africa of the late 1960s onwards the liberation of the oppressed black people was high on the agenda of Black Theology. As a leader of the early South African Black Theology, Buthelezi is concerned about the racial injustice in his country. He urges the churches to join the struggle against it as one people of God. The notions of liberation and the wholeness of life emerge in Buthelezi’s holistic understanding of liberation that involves the inner liberation of the black spirit and the liberation of the economic, social and political aspects of life. Interpreting Tillich’s correlation method in the South African situation, and also paralleling other liberation theologians, Buthelezi takes the existential situation of the people as the starting point for liberation. The gospel has to respond to the existential questions of people. The church is called to work for the liberation of society but it must also be liberated itself. Buthelezi initiated the LWF statement on the status confessionis in South Africa (1977). In line with the statement, he calls for church unity on the human level. For the unity to be true, it has to be experienced on the grassroots’ level. All the three concepts covered urge the church to come down from any ivory tower and out of any spiritual haven it might hide in. A lot of the credibility of the church derives from the behavior of the people. Buthelezi’s concentration on how the people who constitute the church should live their faith leaves less attention to how God constitutes the church. I have labeled Buthelezi’s understanding of the church existential-Christocentric due to the emphasis he lays on the need of the church to take the existential situation of the people seriously and on the other hand, on Christ as the exemplar for the church.