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  • 251.
    Bartoszek, Krzysztof
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Trait evolution with jumps: illusionary normality2017Inngår i: Proceedings of the XXIII National Conference on Applications of Mathematics in Biology and Medicine, 2017, s. 23-28Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Phylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous.This is despite biological intuition that evolution is rather punctuated thangradual. On the other hand, there has been a number of recent proposals of evolutionarymodels with jump components. However, as we are only beginning to understandthe behaviour of branching Ornstein-Uhlenbeck (OU) processes the asymptoticsof branching  OU processes with jumps is an even greater unknown. In thiswork we build up on a previous study concerning OU with jumps evolution on a pure birth tree.We introduce an extinction component and explore via simulations, its effects on the weak convergence of such a process.We furthermore, also use this work to illustrate the simulation and graphic generation possibilitiesof the mvSLOUCH package.

  • 252.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Bartoszek, Wojciech
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    A Noether theorem for stochastic operators on Schatten classes2017Inngår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, nr 2, s. 1395-1412Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that a stochastic (Markov) operator S acting on a Schatten class C-1 satisfies the Noether condition (i.e. S' (A) = A and S' (A(2)) = A(2), where A is an element of C-infinity is a Hermitian and bounded operator on a fixed separable and complex Hilbert space (H, <.,.>)), if and only if S(E-A(G)XEA(G)) = E-A (G)S(X)E-A (G) for any state X is an element of C-1 and all Borel sets G subset of R, where E-A (G) denotes the orthogonal projection coming from the spectral resolution A = integral(sigma(A)) zE(A)(dz). Similar results are obtained for stochastic one-parameter continuous semigroups.

  • 253.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Bartoszek, Wojciech
    Gdansk University of Technology, Poland.
    On the Time Behaviour of Okazaki Fragments2006Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 43, nr 2, s. 500-509Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.

  • 254.
    Bartoszek, Krzysztof
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Analys och sannolikhetsteori.
    Domsta, Joachim
    State Univ Appl Sci Elblag, Krzysztof Brzeski Inst Appl Informat, Ul Wojska Polskiego 1, PL-82300 Elblag, Poland.
    Pulka, Malgorzata
    Gdansk Univ Technol, Dept Probabil & Biomath, Ul Narutowicza 11-12, PL-80233 Gdansk, Poland.
    Weak Stability of Centred Quadratic Stochastic Operators2019Inngår i: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, Vol. 42, nr 4, s. 1813-1830Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offsprings trait is equal to an additively perturbed arithmetic mean of the parents traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.

    Fulltekst (pdf)
    Weak Stability of Centred Quadratic Stochastic Operators
  • 255.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology.
    Izydorek, Bartosz
    Gdansk University of Technology.
    Ratajczak, Tadeusz
    Gdansk University of Technology, Poland.
    Skokowski, Jaroslaw
    Medical University of Gdansk, Poland.
    Szwaracki, Karol
    Gdansk University of Technology, Poland.
    Tomczak, Wiktor
    Gdansk University of Technology, Poland.
    Neural Network Breast Cancer Relapse Time Prognosis2006Inngår i: ASO Summer School 2006 abstract book Ostrzyce 30.06-2.07. 2006 / [ed] J. Skokowski and K. Drucis, 2006, s. 8-10Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    This paper is a result of a project at the Faculty of Electronics, Telecommunication and Computer Science (Technical University of Gdansk). The aim of the project was to create a neural network to predict the relapsetime of breast cancer. The neural network was to be trained on data collected over the past 20 years by dr. Jarosław Skokowski. The data includes 439 patient records described by about 40 parameters. For our neuralnetwork we only considered 6 medically most significant parameters the number of nodes showing evidence of cancer, size of tumour (in mm.), age, bloom score, estrogen receptors and proestrogen receptors and the relapsetime as the outcome. Our neural network was created in the MATLAB environment.

  • 256.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Jones, Graham
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden / Department of Biological and Environmental Science, University of Gothenburg, Gothenburg, Sweden.
    Oxelman, Bengt
    Department of Biological and Environmental Science, University of Gothenburg, Gothenburg, Sweden.
    Sagitov, Serik
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Time to a single hybridization event in a group of species with unknown ancestral history2013Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 322, s. 1-6Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove results about the distribution of the time of the hybridization event. In particular we calculate a formula for all moments, and show that under various conditions, the distribution tends to an exponential with rate twice that of the birth rate for the Yule process.

  • 257.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.
    Krzeminski, Michal
    Gdansk University of Technology.
    Critical case stochastic phylogenetic tree model via the Laplace transform2014Inngår i: Demonstratio Matematicae, ISSN 0420-1213, Vol. 47, nr 2, s. 474-481Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both in uenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this we correct the proof of Liggett and Schinazi (2009) in the critical case.

  • 258.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Krzeminski, Michal
    Gdansk University of Technology.
    Skokowski, Jaroslaw
    Medical University of Gdansk.
    Survival time prognosis under a Markov model of cancer development2010Inngår i: Proceedings of the XVI National Conference Applications of Mathematics to Biology and Medicine, Krynica, Poland, September 14–18, 2010 / [ed] M. Ziółko, M. Bodnar and E. Kutafina, 2010, s. 6-11Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this study we look at a breast cancer data set of women from the Pomerania region collected in the year 1987- 1992 in the Medical University of Gdansk.We analyze the clinical risk factors in conjunction with a Markov model of cancer development. We evaluate Artificial Neural Network (ANN) survival time prediction (which was done on this data set in a previous study) via a simulation study.

  • 259.
    Bartoszek, Krzysztof
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten.
    Lio, Pietro
    Univ Cambridge, England.
    MODELLING TRAIT-DEPENDENT SPECIATION WITH APPROXIMATE BAYESIAN COMPUTATION2019Inngår i: ACTA PHYSICA POLONICA B PROCEEDINGS SUPPLEMENT, JAGIELLONIAN UNIV , 2019, Vol. 12, nr 1, s. 25-47Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Phylogeny is the field of modelling the temporal discrete dynamics of speciation. Complex models can nowadays be studied using the Approximate Bayesian Computation approach which avoids likelihood calculations. The fields progression is hampered by the lack of robust software to estimate the numerous parameters of the speciation process. In this work, we present an R package, pcmabc, publicly available on CRAN, based on Approximate Bayesian Computations, that implements three novel phylogenetic algorithms for trait-dependent speciation modelling. Our phylogenetic comparative methodology takes into account both the simulated traits and phylogeny, attempting to estimate the parameters of the processes generating the phenotype and the trait. The user is not restricted to a predefined set of models and can specify a variety of evolutionary and branching models. We illustrate the software with a simulation-reestimation study focused around the branching Ornstein-Uhlenbeck process, where the branching rate depends non-linearly on the value of the driving Ornstein-Uhlenbeck process. Included in this work is a tutorial on how to use the software.

  • 260.
    Bartoszek, Krzysztof
    et al.
    Mathematical Statistics, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
    Liò, Pietro
    Computer Laboratory, University of Cambridge Cambridge, United Kingdom.
    Sorathiya, Anil
    Computer Laboratory, University of Cambridge Cambridge, United Kingdom.
    Influenza differentiation and evolution2010Inngår i: Acta Physica Polonica B Proceedings Supplement, 2010, Vol. 3, s. 417-452, artikkel-id 2Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The aim of the study is to do a very wide analysis of HA, NA and M influenza gene segments to find short nucleotide regions,which differentiate between strains (i.e. H1, H2, ... e.t.c.), hosts, geographic regions, time when sequence was found and combination of time and region using a simple methodology. Finding regions  differentiating between strains has as its goal the construction of a Luminex microarray which will allow quick and efficient strain recognition. Discovery for the other splitting factors could shed lighton structures significant for host specificity and on the history of influenza evolution. A large number of places in the HA, NA and M gene segments were found that can differentiate between hosts, regions, time and combination of time and region. Also very good differentiation between different Hx strains can be seen.We link one of our findings to a proposed stochastic model of creation of viral phylogenetic trees.

  • 261.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Pienaar, Jason
    Department of Genetics, University of Pretoria, Pretoria 0002, South Africa.
    Mostad, Petter
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
    Andersson, Staffan
    Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden.
    Hansen, Thomas F.
    CEES, Department of Biology, University of Oslo, Oslo, Norway.
    A phylogenetic comparative method for studying multivariate adaptation2012Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 314, s. 204-215Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Phylogenetic comparative methods have been limited in the way they model adaptation. Although some progress has been made, there are still no methods that can fully account for coadaptationbetween traits. Based on Ornstein-Uhlenbeck (OU) models of adaptive evolution, we present a method,with R implementation, in which multiple traits evolve both in response to each other and, as inprevious OU models, to fixed or randomly evolving predictor variables. We present the interpretation ofthe model parameters in terms of evolutionary and optimal regressions enabling the study of allometric and adaptive relationships between traits. To illustrate the method we reanalyze a data set of antlerand body-size evolution in deer (Cervidae).

  • 262.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pietro, Lio'
    Computer Laboratory , University of Cambridge, Cambridge, Un ited Kingdom.
    A novel algorithm to reconstruct phylogenies using gene sequences and expression data2014Inngår i: International Proceedings of Chemical, Biological & Environmental Engineering; Environment, Energy and Biotechnology III, 2014, Vol. 70, s. 8-12Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Phylogenies based on single loci should be viewed with caution and the best approach for obtaining robust trees is to examine numerous loci across the genome. It often happens that for the same set of species trees derived from different genes are in conflict between each other. There are several methods that combine information from different genes in order to infer the species tree. One novel approach is to use informationfrom different -omics. Here we describe a phylogenetic method based on an Ornstein–Uhlenbeck process that combines sequence and gene expression data. We test our method on genes belonging to the histidine biosynthetic operon. We found that the method provides interesting insights into selection pressures and adaptive hypotheses concerning gene expression levels.

  • 263.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.
    Pulka, Malgorzata
    Department of Probability and Biomathematics, Gdánsk University of Technology, Gdánsk, Poland.
    Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait2013Inngår i: Proceedings of the 19th National Conference on Applications of Mathematics in Biology and Medicine / [ed] Katarzyna D. Lewandowska and Piotr Bogús, 2013, s. 19-24Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introducedand studied recently. In the present work we discuss biological interpretations that can be attributedto them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.

  • 264.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pulka, Malgorzta
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Asymptotic properties of quadratic stochastic operators acting on the L1 space2015Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 114, s. 26-39Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours andthese have been introduced and studied recently in the l1 space. It turns out that inprinciple most of the results can be carried over to the L1 space. However, due to topologicalproperties of this space one has to restrict in some situations to kernel quadratic stochasticoperators. In this article we study the uniform and strong asymptotic stability of quadratic stochastic operators acting on the L1 space in terms of convergence of the associated (linear)nonhomogeneous Markov chains.

  • 265.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Pułka, Małgorzata
    Department of Probability and Biomathematics, Gdańsk University of Technology, Gdańsk, Poland.
    Prevalence Problem in the Set of Quadratic StochasticOperators Acting on L12018Inngår i: Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, Vol. 41, nr 1, s. 159-173Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper is devoted to the study of the problem of prevalence in the classof quadratic stochastic operators acting on the L1 space for the uniform topology.We obtain that the set of norm quasi-mixing quadratic stochastic operators is a denseand open set in the topology induced by a very natural metric. This shows the typicallong-term behaviour of iterates of quadratic stochastic operators.

  • 266.
    Bartoszek, Krzysztof
    et al.
    Uppsala universitet, Tillämpad matematik och statistik.
    Sagitov, Serik
    A consistent estimator of the evolutionary rate2015Inngår i: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 371, s. 69-78Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate 2, conditioned on the observed number of particles to be equal to n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance sigma(2). In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator 4 of the evolutionary rate rho(2) - sigma(2)/lambda. The estimator R-n(2) is proportional to the sample variance S-n(2) computed from n trait values. We find an approximate formula for the standard error of R-n(2), based on a neat asymptotic relation for the variance of S-n(2). (C) 2015 Elsevier Ltd. All rights reserved.

  • 267.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Uppsala University, Uppsala, Sweden.
    Sagitov, Serik
    Chalmers University of Technology and the Unversity of Gothenburg, Sweden.
    Phylogenetic confidence intervals for the optimal trait value2015Inngår i: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, nr 4, s. 1115-1132Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider a stochastic evolutionary model for a phenotype developing amongst n related species with unknown phylogeny. The unknown tree ismodelled by a Yule process conditioned on n contemporary nodes. The trait value is assumed to evolve along lineages as an Ornstein–Uhlenbeck process. As a result, the trait values of the n species form a sample with dependent observations. We establish three limit theorems for the samplemean corresponding to three domains for the adaptation rate. In the case of fast adaptation, we show that for large n the normalized sample mean isapproximately normally distributed. Using these limit theorems, we develop novel confidence interval formulae for the optimal trait value.

  • 268.
    Bartoszek, Krzysztof
    et al.
    Gdansk University of Technology, Poland.
    Signerska, Justyna
    Gdansk University of Technology, Poland.
    Moments of the Distribution of Okazaki Fragments2006Inngår i: Rose–Hulman Undergraduate Mathematics Journal, Vol. 7, nr 2, s. 1-5Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper is a continuation of Bartoszek & Bartoszek (2006) who provide formulae for the probability distributions of the number of Okazaki fragments at time t during the process of DNA replication. Given the expressions for the moments of the probability distribution of the number of Okazaki fragments at time t in the recursive form, we evaluated formulae for the third and fourth moments, using Mathematica, and obtained results in explicit form. Having done this, we calculated the distribution’s skewness and kurtosis.

  • 269.
    Bartoszek, Krzysztof
    et al.
    Department of Mathematics, Gdansk University of Technology, Gdansk, Poland.
    Signerska, Justyna
    Department of Mathematics, Gdansk University of Technology, Gdansk, Poland.
    The Fundamental Group, Covering Spaces and Topology in Biology2006Inngår i: Conference materials 9th International Workshop for Young Mathematicians "Topology", 2006, s. 19-29Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Abstract. We give a short introduction to homotopy theory. We pass to the concepts of a pointed space (X, x0), the fundamental group of X, a simply connected space (with the example of the space contractible to a point), introduce basic concepts of covering spaces (e.g. covering map/space, fiber over x, Path lifting Theorem). With the use of the exponential map and the idea of the index of a loop, we show that the fundamental group of the circle S1 is isomorphic to the integers Z with addition. We mention some other interesting fundamental groups (e.g. the fundamental group of a torus or of thefigure eight). We also present some very interesting applications of topological concepts in Molecular Biology.

  • 270.
    Bartoszek, Krzysztof
    et al.
    Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg.
    Stokowska, Anna
    University of Gothenburg.
    Performance of pseudo-likelihood estimator in modelling cells' proliferation with noisy measurements2010Inngår i: Conference proceedings from the 12th International Workshop for Young Mathematicians "Probability and Statistics", Krakow, Poland, 20th till 26th September 2009, 2010, s. 21-42Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    Branching processes are widely used to describe cell development and proliferation. Currently parameter estimation is studied in mathematical models describing the dynamics of cell cultures where we can get very accurate measurements of cell counts. In vivo samples we will not have this accuracy, here the noise levels can be very significant. We will study a newly proposed pseudo-likelihood estimator of a multitype Bellman-Harris process modelling cell development and see how it performs under noisy measurements of cell counts.

  • 271.
    Basarab-Horwath, Peter
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lie algebras and classification of partial differential equations2004Inngår i: Symmetry in Nonlinear Mathematical Physics,2004, 2004Konferansepaper (Annet vitenskapelig)
  • 272.
    Basarab-Horwath, Peter
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Gungor, F.
    Istanbul Technical University, Turkey.
    Linearizability for third order evolution equations2017Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, nr 8, artikkel-id 081507Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence of an infinite-dimensional symmetry group. Linearizing transformations for this class are found using symmetry structure and local conservation laws. A number of special cases as examples are discussed. Their transformation to equations within the same class by differential substitutions and connection with KdV and mKdV equations is also reviewed in this framework. Published by AIP Publishing.

  • 273.
    Basarab-Horwath, Peter
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lahno, V
    Group classification of the general quasi-linear wave equation: invance under low-dimensional Lie algebras2004Rapport (Annet vitenskapelig)
  • 274.
    Basarab-Horwath, Peter
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Lahno, V.
    Magda, O.
    The structure of Lie algebras and the classification problem for partial differential equations2004Inngår i: Proceedings of Institute of Mathematics of NAS of Ukraine.Mathematics and its Applications, Vol. 50, s. 40-46Artikkel i tidsskrift (Fagfellevurdert)
  • 275.
    Bastani, Spencer
    et al.
    Linköpings universitet, Matematiska institutionen.
    Andersson, Olov
    Linköpings universitet, Matematiska institutionen.
    Stochastic Optimization in Dynamic Environments: with applications in e-commerce2007Independent thesis Advanced level (degree of Magister), 20 poäng / 30 hpOppgave
    Abstract [en]

    In this thesis we address the problem of how to construct an optimal algorithm for displaying banners (i.e advertisements shown on web sites). The optimization is based on the revenue each banner generates, with the aim of selecting those banners which maximize future total revenue. Banner optimality is of major importance in the e-commerce industry, in particular on web sites with heavy traffic. The 'micropayments' from showing banners add up to substantial profits due to the large volumes involved. We provide a broad, up-to-date and primarily theoretical treatment of this global optimization problem. Through a synthesis of mathematical modeling, statistical methodology and computer science we construct a stochastic 'planning algorithm'. The superiority of our algorithm is based on empirical analysis conducted by us on real internet-data at TradeDoubler AB, as well as test-results on a selection of stylized data-sets. The algorithm is flexible and adapts well to new environments.

    Fulltekst (pdf)
    FULLTEXT01
  • 276.
    Becirovic, Ema
    Linköpings universitet, Institutionen för systemteknik, Kommunikationssystem.
    On Social Choice in Social Networks2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Kollektiva beslut blir en del av vardagen när grupper av människor står inför val. Vi anpassar ofta våra personliga övertygelser med hänsyn till våra vänner. Vi är naturligt beroende av lyckan hos dem som står oss nära.

    I det här exjobbet undersöker vi en befintlig empatimodell som används för att välja en vinnare från en uppsättning alternativ genom att använda poängbaserade omröstningsprocedurer. Vi visar att en liten modifikation av modellen är tillräcklig för att kunna använda överlägsna omröstningsprocedurer som bygger på parvisa jämförelser av alternativen.

    Sammanfattningsvis visar vi att det i grunden inte finns någon anledning att använda poängbaserade omröstningsprocedurer i de föreslagna modellerna, eftersom ett mer önskvärt resultat uppnås genom att använda de överlägsna omröstningsprocedurerna.

    Fulltekst (pdf)
    fulltext
  • 277.
    Beckius, Peter
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling.
    Hübel, Alexander
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling.
    Vädrets påverkan på försäljningen inom svensk dagligvaruhandel: En studie om vädrets påverkan på ICA:s försäljning2010Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [ar]

    ICA is the largest general dealer in the Swedish market as well as the largest supplier to the independent ICA-dealers. The principal and one of the biggest stakeholders of this thesis is the department Supply Chain Development who is responsible for the development of ICA’s Supply Chain.

    The purpose of this study is to examine how ICA’s sales are affected by weather and to make recommendations on how ICA should proceed with its work regarding this issue. By leveraging their forecasts by including weather, ICA hopes that their logistical metrics amount of spoilage, service levels and number of inventory days will improve. This thesis describes how ICA is working with weather currently, and furthermore it discusses the existing literature within this area. Extensive statistical surveys have been conducted in order to identify the products that are affected by weather, and to examine how they are affected by different weather variables. Finally, the thesis gives recommendations to ICA on how they can improve their forecasting by taking this study’s results into account.

    Presently ICA has no consistent approach when it comes to considering weather’s impact on sales. Each individual product planner uses his own experience and gut feeling and there is no central guidance or other quantitative information there to help them.

    This thesis is organised around two major statistical studies. First, a correlation study examines the correlation between sales and deviation from mean temperature. The weather parameter was selected following recommendations from earlier studies and from SMHI - the national weather institute in Sweden. The study was conducted on ICA’s entire assortment and identified which items that were affected by weather. These turned out to be about a hundred in number and were affected mainly during the summer; however a few items were also affected in the winter. Most of the affected items were rather logical regarding weather’s effects on sales and have also been pointed out by planners as products that are likely to be affected by weather. Following that, several regression analyses were conducted on the selected weather affected assortment.

    The regression analyses were conducted with various combinations of one or more weather parameters as explanatory variables. Surprisingly, in most cases the deviation from mean temperature alone was the parameter that best explained the variance in sales figures. The result or output of this thesis is a value for the expected change in sales for a selected assortment, given a change in deviation from mean temperature.

    The recommendations given at the end of this thesis explains how ICA in a simple and cost effective way could implement the study's results in their daily work. The proposal is to divide the work by what should be done centrally by the forecasting department, and by what should be done individually by each planner. The forecasting department should regularly collect weather forecasts over different time periods, calculate the deviation from mean temperature and distribute it to the supply planner. After that, it is up to the supply planners on how to best take advantage of this information by taking into account other unique factors affecting each category, such as campaigns, holidays and daily indexes that in many cases have more effect on sales than the weather.

    Fulltekst (pdf)
    FULLTEXT01
  • 278. Bestill onlineKjøp publikasjonen >>
    Bendtsen, Marcus
    Linköpings universitet, Institutionen för datavetenskap, Databas och informationsteknik. Linköpings universitet, Tekniska fakulteten.
    Gated Bayesian Networks2017Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    Bayesian networks have grown to become a dominant type of model within the domain of probabilistic graphical models. Not only do they empower users with a graphical means for describing the relationships among random variables, but they also allow for (potentially) fewer parameters to estimate, and enable more efficient inference. The random variables and the relationships among them decide the structure of the directed acyclic graph that represents the Bayesian network. It is the stasis over time of these two components that we question in this thesis.

    By introducing a new type of probabilistic graphical model, which we call gated Bayesian networks, we allow for the variables that we include in our model, and the relationships among them, to change overtime. We introduce algorithms that can learn gated Bayesian networks that use different variables at different times, required due to the process which we are modelling going through distinct phases. We evaluate the efficacy of these algorithms within the domain of algorithmic trading, showing how the learnt gated Bayesian networks can improve upon a passive approach to trading. We also introduce algorithms that detect changes in the relationships among the random variables, allowing us to create a model that consists of several Bayesian networks, thereby revealing changes and the structure by which these changes occur. The resulting models can be used to detect the currently most appropriate Bayesian network, and we show their use in real-world examples from both the domain of sports analytics and finance.

    Fulltekst (pdf)
    fulltext
    Download (pdf)
    omslag
    Download (jpg)
    presentationsbild
  • 279.
    Bengtsson, Ingemar
    et al.
    Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
    Bruzda, Wojciech
    Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland.
    Ericsson, Åsa
    Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
    Larsson, Jan-Åke
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Tillämpad matematik.
    Tadej, Wojciech
    Wydział Matematyczno-Przyrodniczy, Szkoła Nauk Ścisłych, Universytet Kardynała Stefana Wyszyńskiego, Warszawa, Poland.
    Zyczkowski, Karol
    Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland and Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warszawa, Poland.
    Mutually unbiased bases and Hadamard matrices of order six2007Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, nr 5, s. 052106-1-052106-21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We report on a search for mutually unbiased bases (MUBs) in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organize our results. Finally, we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.

    Fulltekst (pdf)
    Mutually unbiased bases and Hadamard matrices of order six
  • 280.
    Bengtsson, Martin
    Linköpings universitet, Matematiska institutionen.
    Analytical Expressions for the Hawking Mass in slowly rotating Kerr and Kerr-Newman Space-times2007Independent thesis Advanced level (degree of Magister), 20 poäng / 30 hpOppgave
    Abstract [en]

    Penrose's inequality which relates the total mass of a space-time containing a black hole with the area of the event horizon, is a yet unproven condition that is required for the cosmic censorship hypothesis. It is believed that the inequality could be proved by using properties of the Hawking mass. This thesis gives analytical expressions for the Hawking mass in slowly rotating Kerr and Kerr-Newman space-times. It is also shown that the expressions are monotonically increasing, a result that does not contradict Penrose's inequality.

    Fulltekst (pdf)
    FULLTEXT01
  • 281.
    Bennevall, Marcus
    Linköpings universitet, Matematiska institutionen.
    Creativity in Mathematics Curricula – An International Comparison between Singapore, Hong Kong, Sweden, and Norway2017Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    Studies have shown that creative mathematically founded reasoning (CMR) outperforms algorithmic reasoning (AR) in regards to retention and (re)construction of knowledge. This suggests that creativity should be encouraged in national high-school mathematics curricula. The aim of the present study is to compare how creativity is framed in different national high-school mathematics curricula, using the following definition: creativity is the characteristics of people, processes, and environments which lead to new and original products that are useful or otherwise attractive to an individual or a society. Utilizing content and discourse analysis, the present study thus contrasts how the high-school mathematics curricula of Singapore, Hong Kong, Sweden, and Norway handle and value creativity, and also examines which role creativity takes in each curricula.

    Findings suggest that Singapore’s curriculum emphasizes creativity the most, and frequently does so in relation to assessment. Hong Kong’s curriculum is found to emphasize creativity in diverse ways, often using words with connotations to playfulness. Analysis of Sweden’s curriculum indicates a relatively minute focus on creativity, tending to put it in a teacher-centered context. A feature of Norway’s curriculum is an increasing emphasis on creativity as courses approach tertiary education. This also suggests a rising value of creativity in its curriculum. A similar though not as pronounced trajectory is found also in Singapore’s curriculum. In the Asian and Norwegian curricula, creativity is expressed both as a means and an end, while in Sweden’s curriculum it is only seen as an end.

    The results are discussed in terms of potential reasons for the prominent national features, and the study also includes an evaluation of the aptness of the suggested definition of creativity, a review of the limitations of the study, as well as propositions for further research. Finally, two recommendations are given to the National Agency for Education in Sweden – Skolverket – based on the results of the study: 1) diversify the emphasis on creativity in the curriculum, and 2) ensure alignment between what teachers value and what Skolverket values with respect to creativity.

    Fulltekst (pdf)
    fulltext
  • 282.
    Bennevall, Marcus
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.
    Cultivating Creativity in the Mathematics Classroom using Open-ended Tasks: A Systematic Review2016Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    Creativity is an ever relevant concept in problem-solving. Indeed, one could argue that no problem is really problematic unless it requires creative thinking; such problems can be solved by simply applying known facts and employing suitable algorithms. Yet, that is exactly how many tasks in mathematics textbooks are structured today. The present study aims to find other tasks, which can infuse creativity in the mathematics classroom. Special attention is turned towards a class of tasks known as open-ended tasks because of their creative potential. A literature review spanning 70 sources yields 17 types of open-ended tasks, and these are subsequently exemplified, classified, analyzed, and discussed from a teacher’s perspective.

    Fulltekst (pdf)
    Cultivating Creativity in the Mathematics Classroom using Open-ended Tasks: A Systematic Review
  • 283.
    Berberovic, Adnan
    et al.
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi.
    Eriksson, Alexander
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi.
    A Multi-Factor Stock Market Model with Regime-Switches, Student's T Margins, and Copula Dependencies2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    Investors constantly seek information that provides an edge over the market. One of the conventional methods is to find factors which can predict asset returns. In this study we improve the Fama and French Five-Factor model with Regime-Switches, student's t distributions and copula dependencies. We also add price momentum as a sixth factor and add a one-day lag to the factors. The Regime-Switches are obtained from a Hidden Markov Model with conditional Student's t distributions. For the return process we use factor data as input, Student's t distributed residuals, and Student's t copula dependencies. To fit the copulas, we develop a novel approach based on the Expectation-Maximisation algorithm. The results are promising as the quantiles for most of the portfolios show a good fit to the theoretical quantiles. Using a sophisticated Stochastic Programming model, we back-test the predictive power over a 26 year period out-of-sample. Furthermore we analyse the performance of different factors during different market regimes.

    Fulltekst (pdf)
    berberovic_eriksson_masterthesis
  • 284.
    Berg, Jens
    Uppsala universitet, Avdelningen för beräkningsvetenskap.
    Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems2013Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which method that is suitable. In this thesis, we focus on the finite difference method which is conceptually easy to understand, has high-order accuracy, and can be efficiently implemented in computer software.

    We use the finite difference method on summation-by-parts (SBP) form, together with a weak implementation of the boundary conditions called the simultaneous approximation term (SAT). Together, SBP and SAT provide a technique for overcoming most of the drawbacks of the finite difference method. The SBP-SAT technique can be used to derive energy stable schemes for any linearly well-posed initial boundary value problem. The stability is not restricted by the order of accuracy, as long as the numerical scheme can be written in SBP form. The weak boundary conditions can be extended to interfaces which are used either in domain decomposition for geometric flexibility, or for coupling of different physics models.

    The contributions in this thesis are twofold. The first part, papers I-IV, develops stable boundary and interface procedures for computational fluid dynamics problems, in particular for problems related to the Navier-Stokes equations and conjugate heat transfer. The second part, papers V-VI, utilizes duality to construct numerical schemes which are not only energy stable, but also dual consistent. Dual consistency alone ensures superconvergence of linear integral functionals from the solutions of SBP-SAT discretizations. By simultaneously considering well-posedness of the primal and dual problems, new advanced boundary conditions can be derived. The new duality based boundary conditions are imposed by SATs, which by construction of the continuous boundary conditions ensure energy stability, dual consistency, and functional superconvergence of the SBP-SAT schemes.

  • 285.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    A stable and dual consistent boundary treatment using finite differences on summation-by-parts form2012Inngår i: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-posed and the discrete problem is stable and spatially dual consistent. These two features result in a superconvergent functional, in the sense that the order of accuracy of the functional is provably higher than that of the solution.

    Fulltekst (pdf)
    fulltext
  • 286.
    Berg, Jens
    et al.
    Uppsala University, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations2014Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 259, s. 135-153Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we derive new farfield boundary conditions for the time-dependent Navier–Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier–Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations.

    We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.

    Fulltekst (pdf)
    fulltext
  • 287.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Duality based boundary treatment for the Euler and Navier-Stokes equations2013Inngår i: AIAA Aerospace Sciences - Fluid Sciences Event, 2013, s. 1-19Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    In this paper we construct well-posed boundary conditions for the compressible Euler and Navier-Stokes equations in two space dimensions. When also considering the dual equations, we show how to construct the boundary conditions so that both the primal and dual problems are well-posed. By considering the primal and dual problems simultaneously, we construct energy stable and dual consistent finite difference schemes on summation-by-  parts form with weak imposition of the boundary conditions.

    According to linear theory, the stable and dual consistent discretization can be used to compute linear integral functionals from the solution at a superconvergent rate. Here we evaluate numerically the superconvergence property for the non-linear Euler and Navier{ Stokes equations with linear and non-linear integral functionals.

    Fulltekst (pdf)
    fulltext
  • 288.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, SE-751 05, Uppsala, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    On the impact of boundary conditions on dual consistent finite difference discretizations2013Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 236, s. 41-55Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we derive well-posed boundary conditions for a linear incompletely parabolic system of equations, which can be viewed as a model problem for the compressible Navier{Stokes equations. We show a general procedure for the construction of the boundary conditions such that both the primal and dual equations are wellposed.

    The form of the boundary conditions is chosen such that reduction to rst order form with its complications can be avoided.

    The primal equation is discretized using finite difference operators on summation-by-parts form with weak boundary conditions. It is shown that the discretization can be made energy stable, and that energy stability is sufficient for dual consistency.

    Since reduction to rst order form can be avoided, the discretization is significantly simpler compared to a discretization using Dirichlet boundary conditions.

    We compare the new boundary conditions with standard Dirichlet boundary conditions in terms of rate of convergence, errors and discrete spectra. It is shown that the scheme with the new boundary conditions is not only far simpler, but also has smaller errors, error bounded properties, and highly optimizable eigenvalues, while maintaining all desirable properties of a dual consistent discretization.

    Fulltekst (pdf)
    fulltext
  • 289.
    Berg, Jens
    et al.
    Division of Scientific Computing, Department of Information Technology, Uppsala University, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains2012Inngår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 62, nr 11, s. 1620-1638Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study the heat and advectionequation in single and multipledomains. The equations are discretized using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices.

    It is shown how the spectrum of the singledomain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. The interface treatments are posed as a function of one parameter, and the impact on the spectrum and discretization error is investigated as a function of this parameter. Finally we briefly discuss the generalization to higher order accurate schemes.

    Fulltekst (pdf)
    fulltext
  • 290.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology.
    Nordström, Jan
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap.
    Stable Robin solid wall boundary conditions for the Navier-Stokes equations2011Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, nr 19, s. 7519-7532Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier–Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.

    The discretization is done using finite differences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of flows ranging from no-slip to almost full slip.

    Fulltekst (pdf)
    fulltext
  • 291.
    Berg, Jens
    et al.
    Uppsala University, Department of Information Technology, Sweden.
    Nordström, Jan
    Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.
    Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form2012Inngår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, nr 20, s. 6846-6860Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Finitedifference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT).

    In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way.

    The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergentfunctionaloutputs.

    Fulltekst (pdf)
    fulltext
  • 292.
    Bergelin, Victor
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Human Activity Recognition and Behavioral Prediction using Wearable Sensors and Deep Learning2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
    Abstract [en]

    When moving into a more connected world together with machines, a mutual understanding will be very important. With the increased availability in wear- able sensors, a better understanding of human needs is suggested. The Dart- mouth Research study at the Psychiatric Research Center has examined the viability of detecting and further on predicting human behaviour and complex tasks. The field of smoking detection was challenged by using the Q-sensor by Affectiva as a prototype. Further more, this study implemented a framework for future research on the basis for developing a low cost, connected, device with Thayer Engineering School at Dartmouth College. With 3 days of data from 10 subjects smoking sessions was detected with just under 90% accuracy using the Conditional Random Field algorithm. However, predicting smoking with Electrodermal Momentary Assessment (EMA) remains an unanswered ques- tion. Hopefully a tool has been provided as a platform for better understanding of habits and behaviour. 

    Fulltekst (pdf)
    fulltext
  • 293. Berggren, Martin
    et al.
    Ekström, Sven-Erik
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    A discontinuous Galerkin extension of the vertex-centered edge-based finite volume method2009Inngår i: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, s. 456-468Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 294.
    Bergholm, Marie
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Gymnasieelevers kommunikativa strategier i matematikklassrummet: En fallstudie av ett smågruppsarbete om derivata2014Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [sv]

    Denna fallstudie belyser gymnasieelevers arbete i små grupper med ett problem kopplat till derivata och syftar till att belysa faktorer som gynnar eller hindrar individernas deltagande i och utveckling av den matematiska kommunikationen i klassrummet. Studien har sin teoretiska förankring i Anna Sfards kommognitiva ramverk, där lärande i matematik ses som deltagande i en matematisk diskurs.

    Under mer än ett årtionde har larmrapporter om svenska elevers bristande kunskaper i matematik avlöst varandra. Forskningsrapporter pekar på olika faktorer bakom denna sjunkande kunskapsutveckling. Den rådande undervisningskulturen, där eleverna i hög grad arbetar individuellt med uppgifter ur läroboken, ses som en förklaring till de försämrade resultaten, och att undervisningen inte ger eleverna möjlighet att utveckla samtliga föreskrivna förmågor i ämnet. För att uppnå detta betonar både forskningsfältet och den nya läroplanen från 2011 vikten av att eleverna kommunicerar i matematik. I detta perspektiv finns ett behov av att belysa skillnader i elevernas deltagande i kommunikationen om matematik, inte minst i samband med lärande i smågrupper, och hur detta antas påverka elevernas förutsättningar till lärande.

    Studiens fokus är riktat mot deltagarnas olika bidrag till gruppens matematiska diskurs, det vill säga då eleverna kommunicerar om matematiska objekt eller processer, och hur dessa påverkar elevernas förutsättningar och deltagande i kommunikationen. Fokus är också riktat mot den kommunikation som handlar om deltagarna i gruppen, vad eleverna gör och hur de värderar varandras sätt att delta i den matematiska diskursen i klassrummet. Denna kommunikation, benämns i ramverket för subjektifiering och antas vara sammankopplad med individens lärande i matematik.

    Datainsamlingsmetoder som använts är intervjuer, audio- och videoinspelningar och användning av audiovisuella pennor för att sammanföra verbal och skriftlig kommunikation. Diskursen ses som den naturliga analysenheten. I analysens första steg studerades den matematiska diskursen avseende skillnader i innehållet i deltagarnas yttranden. I ett andra analyssteg fokuserades på interaktionsflödet i gruppen för att förstå mer av skillnader i varje elevs deltagande och bidrag till kommunikation.

    Studiens resultat visar på stora skillnader avseende deltagande och innehåll i elevernas kommunikation, både på grupp- och individnivå. Elevernas utveckling av den matematiska diskursen gynnas av användningen av flera olika mediatorer för att representera de matematiska objekten. När eleverna erbjuds kopplingar till en tidigare erövrad diskurs, leder det till diskursiva framflyttningar. Eleverna visar sig vidare ha stora svårigheter att tolka och använda det formella matematiska symbolspråket som stöd för matematiserandet. Elevernas tolkning av likhetstecknet, olikhetstecknet och symbolen f´(x) på en processnivå skapar hinder för att utveckla den matematiska diskursen i önskvärd riktning. Den diskurs som handlar om deltagarna och deras egenskaper (identifiering) utgör ca 10 % av samtliga yttranden och är i stort sett samtliga negativa omdömen, ofta använda i syfte att utesluta eller införliva sig själva eller andra från deltagande i matematiserandet.

    Forskningsstudien visar på ett behov av ytterligare kunskap om hur matematiklärare på bästa sätt kan organisera arbete i smågrupper för att öka elevernas engagemang och kvaliteten på elevernas matematiserande. Studien pekar vidare på vikten av att matematiklärare belyser och varierar användningen av olika mediatorer för att representera de matematiska objekt som är föremål för lärandet. Fallstudien belyser även vikten av att bygga upp det tillåtande arbetsklimat där eleverna inte bedömer sig själva och andra, utan istället vågar ställa de frågor som innebär att de blir alltmer delaktiga i den matematiska diskursen. Ett behov framträder av ytterligare forskning riktad mot inte bara mot den bedömning som sker mellan lärare och elev, utan också mot den bedömning som pågår i klassrummet mellan eleverna, vilket kan påverka vilka roller de väljer eller tilldelas i klassrummet. Detta kan antas vara av stor vikt för hur eleverna kommunicerar om matematik med andra deltagare i klassrummet, vilket också kan antas påverka lärandet.

    Fulltekst (pdf)
    Gymnasieelevers kommunikativa strategier i matematikklassrummet: En fallstudie av ett smågruppsarbete om derivata
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  • 295.
    Berglund, Frida
    et al.
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Oskarsson, Mayumi Setsu
    Linköpings universitet, Institutionen för datavetenskap, Statistik.
    Modellering av spårvidd över bandel 119 inom Stambanan genom Övre Norrland: Kandidatuppsats i Statistik och dataanalys2015Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Trafikverket har varit de som ansvarar för underhållet på den svenska järnvägen sedan 2010. För att järnvägen ska vara säker för passagerare och övriga transporter behöver den hållas i gott skick genom regelbundet underhåll. Därför är det viktigt att kontrollera spårgeometriers kvalitet. Spårvidden är en utav de viktigaste mått som varken får vara för bred eller för smal.

    Syftet med denna rapport är att bygga en modell som kan användas för att simulera avvikelsen på normal spårvidd med avseende på spårgeometrier samt spårens egenskaper.

    Avikkelsen från normal spårvidd är en slumpvariabel som vi modellerat med en generaliserad linjär modell och en generaliserad additiv modell. De kan sedan användas för att simulera avvikelsen på normal spårvidd. I studien visas att GAM lyckas förklara en stor del av variationen i avvikelse på normal spårvidd med hjälp av information från spårgeometrier samt spårens egenskaper.

    Fulltekst (pdf)
    fulltext
  • 296.
    Bergman, Tobias
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Läxa i matematik: Vad säger forskningen?: Vilka faktorer påverkar effekten av läxa i matematik?2019Independent thesis Basic level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Denna litteraturstudie undersöker vilka faktorer som påverkar effekten som läxa har på elevers kunskaper i  matematik. Studien visar att läxa är ett komplext fenomen som påverkas av många faktorer och även varierar beroende  på ämne. På grund av komplexiteten begränsas studien till att undersöka effekten av läxa på individnivå. Studien identifierar ett antal faktorer. Dessa faktorer visar sig ha en stark koppling till varandra och är svåra att skilja från varandra. Därför grupperas de i följande tre kategorier: lärarens syfte med läxan, läxans konstruktion samt elevens förutsättning att genomföra läxan. Studien visar även att läxa varken är strikt positiv eller negativ. Faktorer i alla kategorierna kan medföra att  elevens kunskaper påverkas positivt, negativt eller inte alls. Den viktigaste slutsatsen av studien är därför att man som  lärare bör planera sin läxa noggrant, ha ett explicit syfte och att ge tydlig och välgenomtänkt återkoppling

    Fulltekst (pdf)
    fulltext
  • 297. Bestill onlineKjøp publikasjonen >>
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Conformal Einstein spaces and Bach tensor generalization in n dimensions2004Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    In this thesis we investigate necessary and su±cient conditions for an n-dimensional space, n ≥ 4, to be locally conformal to an Einstein space. After reviewing the classical results derived in tensors we consider the four-dimensional spinor result of Kozameh, Newman and Tod. The involvement of the four-dimensional Bach tensor (which is divergence-free and conformally well-behaved) in their result motivates a search for an n-dimensional generalization of the Bach tensor Bab with the same properties. We strengthen a theorem due to Belfagón and Jaén and give a basis (Uab, V ab and Wab) for all n-dimensional symmetric, divergence-free 2-index tensors quadratic in the Riemann curvature tensor. We discover the simple relationship Bab = 1/2Uab + 1/6V ab and show that the Bach tensor is the unique tensor with these properties in four dimensions. Unfortunately we have to conclude, in general that there is no direct analogue in higher dimension with all these properties.

    Nevertheless, we are able to generalize the our-dimensional results due to Kozameh, Newman and Tod to n dimensions. We show that a generic space is conformal to an Einstein space if and only if there exists a vector field satisfying two conditions. The explicit use of dimensionally dependent identities (some of which are newly derived in this thesis) is also exploited in order to make the two conditions as simple as possible; explicit examples are given in five and six dimensions using these tensor identities. For n dimensions, we define the tensors babc and Bab, and we show that their vanishing is a conformal invariant property which guarantees that the space with non-degenerate Weyl tensor is a conformal Einstein space.

    Fulltekst (pdf)
    Conformal Einstein spaces and Bach tensor generalization in n dimensions
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  • 298.
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Conformal Einstein spaces and Bach tensor generalizations in n dimensions2004Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    In this thesis we investigate necessary and sufficient conditions for an n-dimensional space, n ≥ 4, to be locally conformal to an Einstein space. After reviewing the classical results derived in tensors we consider the four-dimensional spinor result of Kozameh, Newman and Tod. The involvement of the four-dimensional Bach tensor (which is divergence-free and conformally well-behaved) in their result motivates a search for an n-dimensional generalization of the Bach tensor Bab with the same properties. We strengthen a theorem due to Belfagón and Jaen and give a basis (Uab = Vab and Wab) for all n-dimensional symmetric, divergence-free 2-index tensors quadratic in the Riemann curvature tensor. We discover the simple relationship Bab = ½Uab + ⅙Vab and show that the Bach tensor is the unique tensor with these properties in four dimensions. Unfortunately we have to conclude, in general that there is no direct analogue in higher dimension with all these properties.

    Nevertheless, we are able to generalize the four-dimensional results due to Kozameh, Newman and Tod to n dimensions. We show that a generic space is conformal to an Einstein space if and only if there exists a vector field satisfying two conditions. The explicit use of dimensionally dependent identities (some of which are newly derived in this thesis) is also exploited in order to make the two conditions as simple as possible; explicit examples are given in five and six dimensions using these tensor identities.

    For n dimensions, we define the tensors 𝔟abc and 𝔅ab, and we show that their vanishing is a conformal invariant property which guarantees that the space with non-degenerate Weyl tensor is a conformal Einstein space.

  • 299.
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Designing, implementing and evaluating mathematical modelling modules at the upper secondary level2009Rapport (Annet vitenskapelig)
    Abstract [en]

    This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.

    The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.

    The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.

    It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.

  • 300.
    Bergman Ärlebäck, Jonas
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-20002009Rapport (Annet vitenskapelig)
    Abstract [en]

    Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.

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