Diss. Uppsala : Uppsala universitet, 2007.

Lic.-avh. Uppsala : Uppsala universitet, 2004.

Diss. Linköping : Linköpings universitet, 2006.

Diss. Uppsala : Uppsala universitet, 2005.

Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 8 uppsatser.

In diabetes mellitus pancreas fails to produce insulin enough to maintain tissue utilisation of blood glucose. To maintain a normalised metabolism many diabetic patients have to provide insulin from injections or an infusion pump. The disease affects some percent of western population. The insulin provided by the patient has to be adjusted to food and physical exercise. This may be achieved by following rules from diabetes professionals, but also by self learning how food, insulin and physical exercise interact and influence the blood glucose. It seems that the patients who have this intuitive knowledge of the interactions are the ones who manages their diabetes treatment best and have the highest quality of life. The learning have, however, been performed by trial and error - to the price of severe inconvenience and bad metabolic control. A combination of computer science and diabetes physiology has resulted in the computer program Särimner. It is created to give the user a possibility to experiment with diabetes treatment. Food, insulin and physical exercise may be varied and the blood glucose is calculated. Sarimner provides a short-cut to obtaining knowledge since it allows experiments, stimulates discussions and let the user by himself formulate and test hypotheses regarding experienced problems. Since Särimner may be adjusted to look more alike an individual, the experiments are driven by the user's own curiosity. He may experiment with situations of importance to himself and finally make himself the expert of his own treatment situation. The way Särimner is designed, allows interested users to get "under the skin" of the model and study details in the physiological processes. This transparency makes it possible to search for explanations to treatment phenomena. One drawback with the model is that it is quite complex and requires some knowledge from a user with the ambition to understand all the processes. To measure the impact of Särimner training, 11 diabetic teenagers were evaluated with respect to metabolic control, emotional adjustment, focus of control, self-esteem and ability to discuss treatment phenomena. No control group was possible to recruit. The results indicated that the education had been useful for some individuals. They increased their knowledge and ability to discuss treatment situations, their sense of control over the diabetes treatment, their self esteem and furthermore Särimner education may have caused a reduction of diabetes related stress. However, an increased level of diabetes related guilt did occur in some individuals, possibly due to either increased knowledge or a more internalised focus of control. The models ability to look alike reality is depending on for which purpose it is used. Even though it would be theoretically possible to fit the model to an individual, such an experiment would not be performable in reality since Särimner requires input data from the physiology which is impossible to measure. The properties of the model are, however, adequate for illustrating several treatment situations on a phenomenological level.

Studiens syfte var att bidra med kunskap om hur läroböcker erbjuder stöd för lärandet i matematik för elever med språkstörning i årskurs 4. Bakgrunden behandlade matematik som språk, behov som elever med språkstörning kan ha, läromedels roll i skolan och tidigare studier i läromedelsanalyser. Det teoretiska ramverket utgick från en tidigare läromedelsanalys med fokus på elever i matematiksvårigheter och redogjorde studiens centrala begrepp som utgjorde kriterier i analysverktyget. Studiens syfte uppnåddes genom en kvalitativ textanalys och erbjuder ett användbart analysverktyg som beskrivs i studiens metod. Studiens resultat indikerade varierande stöd för elever med språkstörning, där en bok erbjöd mer stöd. Båda läroböcker visade begränsat tillgänglighet när det gäller matematiska modeller, samt brister i skriftliga träningsmöjligheter. Resultaten diskuterades angående huruvida läroböckerna möter behoven för elever med språkstörning. Slutsatsen blev att läroböckernas tillgänglighet och träningsmöjligheter bör förbättras, med stöd av lärares och speciallärares avgörande roll att anpassa undervisningen för elever med språkstörning.

This thesis consists of three distinct parts. Part I introduces the basic concepts and the notion of general quadratic term structures (GQTS) essential in some of the following chapters. Part II focuses on credit risk models and Part III studies forward price term structure models using both the classical and the geometrical approach.  Part I is organized as follows. Chapter 1 is divided in two main sections. The first section presents some of the fundamental concepts which are a pre-requisite to the papers that follow. All of the concepts and results are well known and hence the section can be regarded as an introduction to notation and the basic principles of arbitrage theory. The second part of the chapter is of a more technical nature and its purpose is to summarize some key results on point processes or differential geometry that will be used later in the thesis. For finite dimensional factor models, Chapter 2 studies GQTS. These term structures include, as special cases, the affine term structures and Gaussian quadratic term structures previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these GQTS for zero-coupon bond prices. On Part II we focus on credit risk models.   In Chapter 3 we propose a reduced form model for default that allows us to derive closed-form solutions for all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and survival probabilities. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity of default is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk that considers both firm-specific and systematic risk. The model generalizes the attempt of Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering effects. Next, we show how to price CDOs, options on CDOs and how to incorporate the link to currently proposed credit indices. In Chapter 4 we start by presenting a reduced-form multiple default type of model and derive abstract results on the influence of a state variable $X$ on credit spreads when both the intensity and the loss quota distribution are driven by $X$. The aim is to apply the results to a real life situation, namely, to the influence of macroeconomic risks on the term structure of credit spreads. There is increasing support in the empirical literature for the proposition that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort, from the theoretical literature, to develop credit risk models that would take this into account. One explanation might be the additional complexity this leads to, even for the ``treatable'' default intensity models. The goal of this paper is to develop the theoretical framework necessary to deal with this situation and, through numerical simulation, understand the impact of macroeconomic factors on the term structure of credit spreads. In the proposed setup, periods of economic depression are both periods of higher default intensity and lower recovery, producing a business cycle effect. Furthermore, we allow for the possibility of an index volatility that depends negatively on the index level and show that, when we include this realistic feature, the impacts on the credit spread term structure are emphasized. Part III studies forward price term structure models. Forward prices differ from futures prices in stochastic interest rate settings and become an interesting object of study in their own right. Forward prices with different maturities are martingales under different forward measures. This mathematical property implies that the term structure of forward prices is always linked to the term structure of bond prices, and this dependence makes forward price term structure models relatively harder to handle. For finite dimensional factor models, Chapter 5 applies the concept of GQTS to the term structure of forward prices. We show how the forward price term structure equation depends on the term structure of bond prices. We then exploit this connection and show that even in quadratic short rate settings we can have affine term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in the study of forward prices, that the difference between the two term structures may be deterministic in some (non-trivial) stochastic interest rate settings. In Chapter 6 we study a fairly general Wiener driven model for the term structure of forward prices. The model, under a fixed martingale measure, $\Q$, is described by using two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest rates, driven by a multidimensional Wiener process $W$. The second system is an infinite SDE for the term structure of forward prices on some specified underlying asset driven by the same $W$. Since the zero coupon bond volatilities will enter into the drift part of the SDE for these forward prices, the interest rate system is needed as input to the forward price system. Given this setup, we use the Lie algebra methodology of Bj\o rk et al. to investigate under what conditions, on the volatility structure of the forward prices and/or interest rates, the inherently (doubly) infinite dimensional SDE for forward prices can be realized by a finite dimensional Markovian state space model. / Diss. Stockholm : Handelshögskolan, 2006

Den här litteraturstudien handlar om matematisk modellering med fokus på åldersgruppen 9–13 år. Vårt syfte är att undersöka om matematisk modellering är ett fördelaktigt arbetssätt i matematikundervisningen samt hur lärare kan använda sig av matematisk modellering i undervisningen undersöks. Vetenskapligt granskad litteratur analyseras och sammanställs för att jämföra vad olika forskare lyfter fram om matematisk modellering. Olika tidskriftsartiklar, ett konferensbidrag och en doktorsavhandling har analyserats. Resultatet visar både för- och motargument till matematisk modellering i åldrarna 9–13 år. Jämförelserna av forskningen i vårt resultat visar att argumenten för matematisk modellering väger tyngre och stödjs av flera forskare än vad motargumenten gör. Ett viktigt argument som många forskare lyfter fram är att modellering hjälper eleverna att överföra matematiken till verkligheten, för att lösa vardagliga problem och på så vis få förbättrade kunskaper om matematikens tillämpningar.

The roads in our society are in a state of constant degradation. The reasons for this are many, and therefore constructed to have a certain lifetime before being reconstructed. To minimize the cost of maintaining the important transport road network high quality prediction models are needed. This report presents new models for flexible pavement structures for initiation and propagation of fatigue cracks in the bound layers and rutting for the whole structure. The models are based on observations from the Swedish Long Term Pavement Performance (LTPP) database. The intention is to use them for planning maintenance as part of a pavement management system (PMS). A statistical approach is used for the modeling, where both cracking and rutting are related to traffic data, climate conditions, and the subgrade characteristics as well as the pavement structure.