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.

Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.

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.

Holistic Spirituality in the Thinking of Ellen White

Spiritualiteetti viittaa syvälliseen, inhimilliseen ulottuvuuteen ja ominaisuuteen, jonka tarkka määritteleminen on haasteellista, ellei mahdotonta. Sitä vastaa yhtäältä uskonnollisuuden kautta toteutuva, elämän tarkoitukseen ja syvemmän olemuksen etsintään liittyvä hengellisyys, mutta toisaalta myös kaikkea muuta hengen viljelyä ja mielekkään olemisen tavoittelua tarkoittava henkisyys. John Swintonin mukaan hengen ulottuvuus on se inhimilliseen olemukseen kuuluva, dynaaminen elinvoima, joka virkistää ja elävöittää ihmistä ja motivoi häntä etsimään Jumalaa, arvoja, merkitystä, tarkoitusta ja toivoa. Tämä tutkimus nostaa tarkastelun kohteeksi kokonaisvaltaisen hengellisyyden, jolloin huomio kiinnitetään niihin sidoksiin, joiden kautta hengen ulottuvuus liittyy muihin inhimillisen elämän olennaisiin toimintoihin ja näkökulmiin. Tällaisia ovat 1) ajattelu 2) teot ja käytännön toiminta 3) suhteet ja vuorovaikutusverkostot 4) tunteet ja kanssakäymistä ohjaavat asenteet 5) olemassaolon ja olemisen ulottuvuudet. Kokemusten merkitys, arvo ja mielekkyys hahmottuvat juuri hengen alueella, toisin sanoen sisäisesti, hengellisenä ja henkisenä asiana. Tutkimusmateriaalina tässä tutkimuksessa on amerikkalaisen vuosina 1827 1915 eläneen Ellen Whiten kuusi myöhäiskauden teosta vuosilta 1892 1905 ja tutkimusmenetelmänä on käytetty systemaattista analyysiä. Olennaista Whiten tavassa käsitellä uskonnon harjoitukseen liittyviä aiheita on hänen käytännöllinen ja elämän arkeen kiinteästi niveltyvä otteensa. Tutkimus paljastaa, että Martti Lutherin käsitykset ovat merkittävästi vaikuttaneet Whiten ajatteluun. Lähteistä paljastuu samankaltaisuutta hänen näkemystensä ja uusimman suomalaisen Luther-tutkimuksen Martti Lutherin tuotannosta esiin nostaman ajattelutavan välillä. Vaikka teologisen oppineisuuden kannalta White ja Luther ovat eri tasoilla, kummankin käsitys ihmisen ja Jumalan välisen suhteen perusolemuksesta on samankaltainen: Lähtökohtana sille on Jumalan rakkaus ja hänen armostaan lähtenyt toiminta. Toiseksi, ihmisen ja Kristuksen välinen, olemuksellinen yhteys, unio , on perustana sille, että Jumala hyväksyy ihmisen ja huolehtii hänestä nyt ja ikuisesti. Kolmanneksi, tämä ihmisen ja Kristuksen liittoutuminen ja yhdistyminen ilmenee yhteistoimintana ja kumppanuutena yhteisten tavoitteiden saavuttamiseksi maailmassa. White korostaa ihmisen ja Kristuksen välisen hengellisen suhteen vuorovaikutteista ja toiminnallista luonnetta, joka tulee ilmi epäitsekkyytenä, toisten ihmisten ja heidän tarpeittensa huomioimisena sekä myötätuntona ja kykynä asettua toisen asemaan. Terveellistä elämäntapaa ja kasvatusta koskevat ajatuksensa White liittää siihen laaja-alaiseen näkemykseen hengellisyydestä, jonka tavoitteena on ihmisen kokonaisvaltainen hyvinvointi. Hän ei näe spiritualiteettia elämän arjesta irrallisena tai erillisenä saarekkeena, vaan ihmistä kaikessa ohjaavana, voimaannuttavana ja mielekkyyttä tuottavana, ensisijaisena ulottuvuutena. Tutkimuksen kuluessa myös Whiten usein käyttämät Jumalalle antautumisen ja luonteen käsitteet nousevat tarkastelun kohteiksi. Hänen mukaansa ihminen ei tahdonponnistuksillaan yksin pysty tavoittamaan Jumalaa vaan hänen on lakattava Jumalan rakastavan kutsun edessä itse tahtomasta ja suostuttava liittymään Jumalan tahtoon ja tarkoitukseen. Tämä liittyy siihen sisäiseen muutokseen, jota White kuvaa luonteen käsitteen avulla. Jumalan armon vaikuttama tahdon uudelleen suuntaaminen muuttaa ihmisen olemusta, arvoja, asennoitumisen tapaa ja myötätuntoisen vuorovaikutuksen kykyä niin ettei ihminen ole enää aivan sama kuin ennen. Kysymys on toisaalta yhtäkkisestä ja kertakaikkisesta olemuksellisesta muuttumisesta, mutta samalla myös hiljaisesta, elämänmittaisesta kasvusta ja kypsymisestä. Juuri luonteen käsitteen avulla White kuvaa hengellisyyttä ja siihen kuuluvaa sisästä matkaa. Tässä tutkimuksessa spiritualiteettia lähestytään yleisinhimillisenä piirteenä ja ominaisuutena, jolloin huomio ei ole ensisijaisesti yksittäisissä opillisissa käsityksissä tai uskonnollisuuden harjoittamisen muodoissa. Tarkoituksena on luoda kokoava rakenne, jonka puitteissa holistinen spiritualiteetti voidaan selkeämmin hahmottaa ja yksilöidymmin ymmärtää.

Tutoring with higher mathematics and the use of technology

We discuss three approaches to the use of technology as a teaching and learning tool that we are currently implementing for a target group of about one hundred second level engineering mathematics students. Central to these approaches is the underlying theme of motivating relatively poorly motivated students to learn, with the aim of improving learning outcomes. The approaches to be discussed have been used to replace, in part, more traditional mathematics tutorial sessions and lecture presentations. In brief, the first approach involves the application of constructivist thinking in the tertiary education arena, using technology as a computational and visual tool to create motivational knowledge conflicts or crises. The central idea is to model a realistic process of how scientific theory is actually developed, as proposed by Kuhn (1962), in contrast to more standard lecture and tutorial presentations. The second approach involves replacing procedural or algorithmic pencil-and-paper skills-consolidation exercises by software based tasks. Finally, the third approach aims at creating opportunities for higher order thinking via "on-line" exploratory or discovery mode tasks. The latter incorporates the incubation period method, as originally discussed by Rubinstein (1975) and others.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

Studies on Plant Demography: Ranunculus Repens L., R. Bulbosus L. and R. Acris L.: III. A Mathematical Model Incorporating Multiple Modes of Reproduction

This paper presents a comparative population dynamics study of three closely related species of buttercups (Ranunculus repens, R. acris, and R. bulbosus). The study is based on an investigation of the behaviour of the seeds in soil under field conditions and a continuous monitoring of survival and reproduction of some 9000 individual plants over a period of 21/2 years in a coastal grassland in North Wales. The data were analysed with the help of an extension of Leslie's matrix method which makes possible an simultaneous treatment of vegetative and sexual reproduction. It was found that R. repens (a) depends more heavily on vegetative as compared with sexual reproduction, (b) shows indications of negatively density-dependent population regulation, and (c) exhibits little variation in population growth rates from site to site and from one year to the next. In contrast, R. bulbosus (a) depends exclusively on sexual reproduction, (b) shows indications of a positively density-dependent population behaviour, and (c) exhibits great variation in population growth rates from site to site and from one year to the next. R. acris exhibits an intermediate behaviour in all these respects. It is suggested that the attributes of R. repens are those expected of a species inhabiting a stable environment, while R. bulbosus exhibits some of the characteristics of a fugitive species.

The Restless Love of Thinking : The Concept Liebe in Hegel's Philosophy

The German philosopher G.W.F.Hegel (1770–1831) is best known for his idealistic system philosophy, his concept of spirit [Geist] and for his dictum that the existing and the rational overlap. This thesis offers a new perspective: it examines the working of the concept ‘love’ in Hegel’s philosophy by looking at the contexts and function he puts it to, from his earliest writings to the very last lectures he gave. The starting point of the inquiry is that he applied the concept Liebe to different contexts for different purposes, but each time to provide an answer to a specific philosophical problem. His formulation, reformulation and use of ‘love’ give possible solutions to problems the solving of which was crucial to the development of his thought as a whole. The study is divided into three parts, each analysing the different problems and solutions to which Hegel applied the concept of love. The first part, "Love, morality and ethical life", examines these interconnected themes in Hegel’s early work. The main questions he addressed during this period concerned how to unite Kant’s philosophy and the Greek ideal of the good life. In this context, the concept ‘love’ did three things. First, it served to formulate his grounding idea of the relation between unity and difference, or the manifold. Secondly, it was the key to his attempt to base an ideal folk religion on Christianity interpreted as a religion of love. Finally, it provided the means to criticise Kant’s moral philosophy. The question of the moral value of love helped Hegel to break away from Kant’s thought and develop his own theory about love and ethical life. The second part of the study, "Love and the political realm", considers the way 'Liebe' functions in connection with questions concerning the community and political life in Hegel’s work. In addition to questioning the universal applicability of the concept of recognition as a key to his theory of social relations, the chapters focus on gender politics and the way he conceptualised the gender category ‘woman’ through the concept ‘love’. Another line of inquiry is the way the figure of Antigone was used to conceptualise the differentiated spheres of action for men and women, and the part ‘love’ played in Hegel’s description of Antigone’s motives. Thirdly, Hegel’s analogy of the family and the state and the way ‘love’ functions in an attempt to promote understanding of the relation between citizens and the state are examined. The third and final part of the study, "Love as absolute spirit", focuses on ‘love’ within Hegel’s systemic thought and the way he continued to characterise Geist through the language of Liebe up until and including his very last works. It is shown how Liebe functions in his hierarchical organisation of the domains of art, religion and philosophy, and how both art and religion end up in similar structural positions with regard to philosophy. One recurrent theme in the third part is Hegel’s complex relation to Romantic thought. Another line of investigation is how he reconstructed Christianity as a religion of love in his mature work. In striking contrast to his early thought, in his last works Hegel introduced a new concept of love that incorporated negativity, and that could also function as the root of political action.

Re-thinking discourses of teacher professionalism in early childhood education: An Australian perspective

The professionalism of early childhood teachers has been the subject of increasing attention globally for over a decade (Moss, 2006; Osgood, 2012; Urban, 2010. In order to understand ways pre-service early childhood teachers make sense of professionalism, this chapter examines some of the discourses of early childhood teacher professionalism, and focuses on qualifications as one way in which being professional is discursively produced. In particular, the chapter makes visible some of the discursive tensions involved in student intentions to pursue careers in primary school teaching/specialist early childhood teacher in primary school, rather than in the child care sector. In doing so, it makes visible some of the effects of particular discourses of professionalism and the ways they may be taken up by students as they make important career decisions.

An approximate mathematical procedure for the determination of characteristic parameters for a general case in three dimensional photoelasticity

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The logic of data-sense: Thinking through Learning Personalisation

Big Data and Learning Analytics’ promise to revolutionise educational institutions, endeavours, and actions through more and better data is now compelling. Multiple, and continually updating, data sets produce a new sense of ‘personalised learning’. A crucial attribute of the datafication, and subsequent profiling, of learner behaviour and engagement is the continual modification of the learning environment to induce greater levels of investment on the parts of each learner. The assumption is that more and better data, gathered faster and fed into ever-updating algorithms, provide more complete tools to understand, and therefore improve, learning experiences through adaptive personalisation. The argument in this paper is that Learning Personalisation names a new logistics of investment as the common ‘sense’ of the school, in which disciplinary education is ‘both disappearing and giving way to frightful continual training, to continual monitoring'.