Chemical sensing is believed to be the oldest sensory ability. The chemical senses, olfaction and gustation, developed to detect and analyze information in the form of air- or waterborne chemicals, to find food and mates, and to avoid danger. The organization of the olfactory system follows the same principles in almost all living animals, insects as well as mammals. Likely, the similarities are due to parallel evolution – the same type of organisation seems to have arisen more than once. Therefore, the olfactory system is often assumed to be close to optimally designed for its tasks.Paradoxically, the workings of the olfactory system are not yet well known,although several milestone discoveries have been made during the last decades. The most well-known is probably the disovery of the olfactory receptor gene family,announced in 1991 by Linda Buck and Richard Axel. For this and subsequent work, they were awarded a Nobel Prize Award in 2004. This achievement has been of immense value for both experimentalists and theorists, and forms the basis of the current understanding of olfaction. The olfactory system has long been a focus for scientific interest within several fields, both experimental and theoretical, and it has often been used asa model system. And ever since the field of computational neuroscience was founded, the functions of the olfactory system have been investigated through computational modelling. In this thesis, I present several approaches to biologically realistic computational models of parts of the olfactory system, with an emphasis on the earlier stages of the vertebrate olfactory system – olfactory receptor neurons (ORNs) and the olfactory bulb (OB). I have investigated the behaviour of the enzyme CaMKII, which is known to be critical for olfactory adaptation (suppression of constant odour stimuli) in the ORN, using a biochemical model. By constructing several OB models of different size, I have shown that the size of the OB network has an impact on its ability to process noisy information. Taking into account the reported variability of geometrical, electrical and receptor-dependent neuronal characteristics, I have been able to model the frequency response of a population of ORNs. I have used this model to find the key properties that govern most of the ORN population’s response, and investigated some of the possible implications of these key properties in subsequent studies of the ORN population and the OB – what we call the fuzzy concentration coding hypothesis. / Detektion av kemiska ämnen anses allmänt vara den äldsta sensoriska förmågan. De kemiska sinnena, lukt och smak, utvecklades för att upptäcka och analysera kemisk information i form av luft- eller vattenburna ämnen, för att hitta mat och partners, och för att undvika fara. Luktsystemet är organiserat efter samma principer hos nästan alla djurarter, insekter såväl som däggdjur. Troligen beror likheterna på parallell evolution – samma organisation verkar ha uppstått mer än en gång. Därför antas det ofta att luktsystemet är nära optimalt anpassat för sina arbetsuppgifter.Paradoxalt nog är luktsystemets arbetsprinciper ännu inte väl kända, även om flera banbrytande framsteg gjorts de senaste decennierna. Det mest välkända är nog upptäckten av genfamiljen av luktreceptorer, som tillkännagavs 1991 av Linda Buck och Rikard Axel. För detta och efterföljande arbete belönades de med Nobelpriset år 2004. Upptäckten har varit mycket värdefull för både experimentalister och teoretiker, och är grunden för vår nuvarande förståelse av luktsystemet. Luktsystemet har länge varit ett fokus för vetenskapligt intresse inom flera fält, experimentella såväl som teoretiska, och har ofta använts som ett modellsystem. Och ända sedan fältet beräkningsneurobiologi grundades har luktsystemet undersökts genom datormodellering. I denna avhandling presenterar jag flera ansatser till biologiskt realistiskaberäkningsmodeller av luktsystemet, med tonvikt på de tidigare delarna av ryggradsdjurens luktsystem – luktreceptorceller och luktbulben. Jag har undersökt beteendet hos enzymet CaMKII, som anses vara kritiskt viktigt för adaptation (undertryckning av ständigt närvarande luktstimuli) i luktsystemet, i en biokemisk modell. Genom att konstruera flera olika stora modeller av luktbulben har jag visat att storleken på luktbulbens cellnätverk påverkar dess förmåga att behandla brusig information. Genom att ta hänsyn till nervcellernas rapporterade variationer i geometriska, elektriska och receptor-beroende karaktärsdrag har jag lyckats modellera svarsfrekvenserna från en population av luktreceptorceller. Jag har använt denna modell för att hitta de nyckelprinciper som styr huvuddelen av luktreceptorneuron-populationens svar, ochundersökt några av de tänkbara konsekvenserna av dessa nyckelprinciper i efterföljande studier av luktreceptorneuron-populationen och luktbulben – det vi kallar ”fuzzy concentration coding”-hypotesen. / QC20100723

This is a study of assessment in mathematics classrooms and assessment is here regarded as a concept with broad boundaries including e.g. diagnostic tests, portfolios, and acts in teacher-student communication. The study’s purpose is to analyse and understand assessment acts in discursive practices in mathematics classroom communication in terms of affordances for students’ active agency and learning. Five mathematics classrooms are visited and the main data consists of video-recordings and written classroom material. In the study, I examine assessment acts, focuses of assessment acts, and roles of semiotic resources (symbols, gestures, speech etc.). With these findings as a basis, four discourses of assessment in mathematics classrooms are construed. A main conclusion is how the construed discourses hold different affordances for students’ active agency and learning. One discourse, “Do it quick and do it right” has similarities to a traditional discourse of assessment described in previous research. In a second discourse, “Anything goes”, students’ performances that can be regarded as mathematically inappropriate are left unchallenged. In both these discourses the affordances for students’ active agency and learning of mathematics are considered low. In a third discourse, “Anything can be up for a discussion”, the focuses of assessment acts are mainly on mathematics processes and available semiotic resources are connected to these focuses. The fourth discourse, “Reasoning takes time”, takes it one step further with a lower pace and an emphasis on mathematics processes such as reasoning and problem-solving. In these two latter discourses the affordances for students’ active agency and learning of mathematics are high. I contend that there is positive power in an increased awareness of discourses like these. The four discourses of this study can be powerful in discussions about, understandings of, and positive changes in assessment practices in mathematics classrooms.

In this thesis we present a new space-time model of interacting agents in the financial market. It is a combination of the Curie-Weiss model and a model introduced by Järpe. We investigate properties such as the critical temperature and magnetization of the system. The distribution of the Hamiltonian function is obtained and a hypothesis test of independence is derived. The results are illustrated in an example based on real data.

This study is based on three models, Markov model, Hidden Markov model and the Radial basis function neural network. A number of work has been done before about application of these three models to the stock market. Though, individual researchers have developed their own techniques to design and test the Radial basis function neural network. This paper aims to show the different ways and precision of applying these three models to predict price processes of the stock market. By comparing the same group of data, authors get different results. Based on Markov model, authors find a tendency of stock market in future and, the Hidden Markov model behaves better in the financial market. When the fluctuation of the stock price index is not drastic, the Radial basis function neural network has a nice prediction.

The focus in this thesis is on the calculations of an empirical null distributionfor likelihood ratio tests testing either separable or double separable covariancematrix structures versus an unstructured covariance matrix. These calculationshave been performed for various dimensions and sample sizes, and are comparedwith the asymptotic χ2-distribution that is commonly used as an approximative distribution. Tests of separable structures are of particular interest in cases when data iscollected such that more than one relation between the components of the observationis suspected. For instance, if there are both a spatial and a temporalaspect, a hypothesis of two covariance matrices, one for each aspect, is reasonable.

One of the major problem faced by banks is how to manage the risk exposure in large portfolios. According to Basel II regulation banks has to measure the risk using Value-at-Risk with confidence level 99%. However, this regulation does not specify the way to calculate Valueat- Risk. The easiest way to calculate Value-at-Risk is to assume that portfolio returns are normally distributed. Altough, this is the most common way to calculate Value-at-Risk, there exists also other methods. The previous crisis shows that the regular methods are unfortunately not always enough to prevent bankruptcy. This paper is devoted to compare the classical methods of estimating risk with other methods such as Cornish-Fisher Expansion (CFVaR) and assuming generalized hyperbolic distribution. To be able to do this study, we estimate the risk in a large portfolio consisting of ten stocks. These stocks are chosen from the NASDAQ 100-list in order to have highly liquid stocks (bluechips). The stocks are chosen from different sectors to make the portfolio welldiversified. To investigate the impact of dependence between the stocks in the portfolio we remove the two most correlated stocks and consider the resulting eight stock portfolio as well. In both portfolios we put equal weight to the included stocks. The results show that for a well-diversified large portfolio none of the risk measures are violated. However, for a portfolio consisting of only one highly volatile stock we prove that we have a violation in the classical methods but not when we use the modern methods mentioned above.

The problem of managing the portfolio provisions is of very high importance for any financial institution. In this paper we provide both static and dynamic models of provisions estimation for the case when the decision about provisions is made at the first moment of time subject to the absence of information and for the case of complete and incomplete information. Also the hedging strategy for the case of the defaultable market is presented in this work as another tool of reducing the risk of default. The default time is modelled as a first-passage time of a standard Brownian motion through a deterministic barrier. Some methods of numerical provision estimation are also presented.

We investigate a certain epidemics model, with and without noise. Some parameter analysis is performed together with computer simulations. The model was presented in Iacus (2008).

A stochastic differential equationdriven by a Brownian motion where the dispersion is determined by a parameter is considered. The parameter undergoes a change at a certain time point. Estimates of the time change point and the parameter, before and after that time, is considered.The estimates were presented in Lacus 2008. Two cases are considered: (1) the drift is known, (2) the drift is unknown and the dispersion space-independent. Applications to Dow-Jones index 1971-1974  and Goldmann-Sachs closings 2005-- May 2009 are given.

We apply some recent numerical solutions to diffusion bridges written in Iacus (2008). One is an approximate scheme from Bladt and S{\o}rensen (2007), another one, from  Beskos et al (2006), is an algorithm which is exact: no numerical error at given grid points!