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  • 2951.
    Tornberg, Anna-Karin
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Engquist, Björn
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Regularization for accurate numerical wave propagation in discontinuous media2006In: Methods and Applications of Analysis, ISSN 1073-2772, E-ISSN 1945-0001, Vol. 13, no 3, p. 247-274Article in journal (Refereed)
    Abstract [en]

    Structured computational grids are the basis for highly efficient numerical approximations of wave propagation. When there are discontinuous material coefficients the accuracy is typically reduced and there may also be stability problems. In a sequence of recent papers Gustafsson et al. proved stability of the Yee scheme and a higher order difference approximation based on a similar staggered structure, for the wave equation with general coefficients. In this paper, the Yee discretization is improved from first to second order by modifying the material coefficients close to the material interface. This is proven in the $L^2$ norm. The modified higher order discretization yields a second order error component originating from the discontinuities, and a fourth order error from the smooth regions. The efficiency of each original method is retained since there is no special structure in the difference stencil at the interface. The main focus of this paper is on one spatial dimension, with the derivation of a second order algorithm for a two dimensional example given in the last section

  • 2952.
    Tornberg, Anna-Karin
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    A numerical method for simulations of rigid fiber suspensions2006In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 215, no 1, p. 172-196Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

  • 2953.
    Touma, Peter
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Greek-efficient Portfolios and Predictability of Powers of Returns2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This paper will introduce the notion of Greek-efficient portfolios as first described in 'Portfolio Selection with Options' by Professor Semyon Malamud (2014). I will discuss the need of introducing an analogy of mean-variance efficient portfolios with stocks to apply to portfolios with options.

    These portfolios will be shown to be replicated by trading contingent claims on stocks paying out powers of returns. As suggested by Malamud (2014), the construction of Greek-efficient portfolios in practice is feasible if the power returns of stocks are predictable. This project finds that squared and cubic returns indeed are predictable by variables observable in the market for stocks in the Nasdaq100 index. The results were however inconclusive for stocks in the larger S&P500 index mainly due to the frequency of changes in the index and scarcity of data for stocks with a less varied option chain.

    Thus, this project suggests that the construction of Greek-efficient portfolios is feasible without having unrealistically high transaction costs.

  • 2954.
    Trost, Johanna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Tail Dependence Considerations for Cross-Asset Portfolios2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Extreme events, heaviness of log return distribution tails and bivariate asymptotic dependence are important aspects of cross-asset tail risk hedging and diversification. These are in this thesis investigated with the help of threshold copulas, scalar tail dependence measures and bivariate Value-at-Risk. The theory is applied to a global equity portfolio extended with various other asset classes as proxied by different market indices. The asset class indices are shown to possess so-called stylised facts of financial asset returns such as heavy-tailedness, clustered volatility and aggregational Gaussianity. The results on tail dependence structure show on lack of strong joint tail dependence, but suitable bivariate dependence models can nonetheless be found and fitted to the data. These dependence structures are then used when concluding about tail hedging opportunities as defined by highly tail correlated long vs short positions as well as diversification benefits of lower estimated Value-at-Risk for cross-asset portfolios than univariate portfolios.

  • 2955.
    Truong, Patrick
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    An exploration of topological properties of high-frequency one-dimensional financial time series data using TDA2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Topological data analysis has been shown to provide novel insight in many natural sciences. To our knowledge, the area is however relatively unstudied on financial data. This thesis explores the use of topological data analysis on one dimensional financial time series. Takens embedding theorem is used to transform a one dimensional time series to an $m$-dimensional point cloud, where $m$ is the embedding dimension. The point cloud of the time series represents the states of the dynamical system of the one dimensional time series. To see how the topology of the states differs in different partitions of the time series, sliding window technique is used. The point cloud of the partitions is then reduced to three dimensions by PCA to allow for computationally feasible persistent homology calculation. Synthetic examples are shown to illustrate the process. Lastly, persistence landscapes are used to allow for statistical analysis of the topological features. The topological properties of financial data are compared with quantum noise data to see if the properties differ from noise. Complexity calculations are performed on both datasets to further investigate the differences between high-frequency FX data and noise. The results suggest that high-frequency FX data differs from the quantum noise data and that there might be some property other than mutual information of financial data which topological data analysis uncovers.

  • 2956.
    Trzetrzelewski, Maciej
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    BPS STATES IN PERTURBATIVE N=4 SYM2008In: Acta Physica Polonica B, ISSN 0587-4254, E-ISSN 1509-5770, Vol. 39, no 12, p. 3439-3447Article in journal (Refereed)
    Abstract [en]

    The partition function of 1/16 BPS states in N = 4 SYM is found using the one loop dilatation operator. The result matches precisely the AdS/CFT prediction, i.e. it coincides with the partition function of the gas of supergravitons in AdS(5) X S-5.

  • 2957.
    Uyanga, Enkhzul
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Wang, Lisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Algorithm that creates productcombinations based on customerdata analysis: An approach with Generalized Linear Modelsand Conditional Probabilities2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This bachelor’s thesis is a combined study of applied mathematical statistics and industrial engineering and management implemented to develop an algorithm which creates product combinations based on customer data analysis for eleven AB. Mathematically, generalized linear modelling, combinatorics and conditional probabilities were applied to create sales prediction models, generate potential combinations and calculate the conditional probabilities of the combinations getting purchased. SWOT analysis was used to identify which factors can enhance the sales from an industrial engineering and management perspective.

    Based on the regression analysis, the study showed that the considered variables, which were sales prices, brands, ratings, purchase countries, purchase months and how new the products are, affected the sales amounts of the products. The algorithm takes a barcode of a product as an input and checks whether if the corresponding product type satisfies the requirements of predicted sales amount and conditional probability. The algorithm then returns a list of possible product combinations that fulfil the recommendations.

  • 2958.
    Vallin, Simon
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Small Cohort Population Forecasting via Bayesian Learning2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A set of distributional assumptions regarding the demographic processes of birth, death, emigration and immigration have been assembled to form a probabilistic model framework of population dynamics. This framework was summarized as a Bayesian network and Bayesian inference techniques are exploited to infer the posterior distributions of the model parameters from observed data. The birth, death and emigration processes are modelled using a hierarchical beta-binomial model from which the inference of the posterior parameter distribution was analytically tractable. The immigration process was modelled with a Poisson type regression model where posterior distribution of the parameters has to be estimated numerically. This thesis suggests an implementation of the Metropolis-Hasting algorithm for this task. Classifi cation of incomings into subpopulations of age and gender is subsequently made using a Dirichlet-multinomial hierarchic model, for which parameter inference is analytically tractable. This model framework is used to generate forecasts of demographic data, which can be validated using the observed outcomes. A key component of the Bayesian model framework used is that is estimates the full posterior distributions of demographic data, which can take into account the full amount of uncertainty when forecasting population growths.

  • 2959. Van den Hoogen, J.
    et al.
    Meijer, Sebastiaan
    KTH, School of Technology and Health (STH), Health Systems Engineering, Health Care Logistics.
    Gaming Simulation Hybrids in the Railway Domain: How Games Impact the Volatility of Innovation Processes2016In: SIMULATION AND GAMING IN THE NETWORK SOCIETY / [ed] Kaneda, T Kanegae, H Toyoda, Y Rizzi, P, SPRINGER-VERLAG SINGAPORE PTE LTD , 2016, p. 291-307Conference paper (Refereed)
    Abstract [en]

    Innovation processes in the railway domain are highly chaotic due to the reciprocal influences of technological, social, and institutional dynamics over time. The ways by which gaming simulation can contribute to these processes is therefore highly context, time, and history dependent. Using three case studies, we explore basic recurrent patterns in these innovation processes and how the employment of gaming simulation has alleviated or attenuated these patterns. For different product architectures that characterize the innovation artifact, different patterns arise in different sequences for the process. We conclude that gaming's main active substance is in the opening up or closing down of technological, social, and institutional spaces. In addition, this impact is again highly moderated by the specific constellation of these spaces when a game is designed, executed, and analyzed. Broadly we see that in stable times, gaming simulation is able to decrease stability and thereby front-load much of the volatility otherwise found at later stages of the innovation process. In contrast, gaming simulation's ability to decrease volatility in volatile times is more problematic.

  • 2960.
    van Eesbeeck, Laurent
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Solving Rubik’s Cube with Non-Standard Moves2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Still another thesis on Rubik’s cube? Is there still something new to write on that puzzle? In this document, we approach the cube with a rather unusual question: “how would you solve the cube if, instead of using the 6 classical rotations, you were restricted to a set of arbitrary moves?” To answer that question, we will dive into group theory.

    Inspired by some previous work on the factorization of the symmetric group, we have developed an algorithm that answers our initial question. However, being able to solve the cube with any set of moves has a trade-off: while some algorithms solve the cube in 20 moves, ours requires several thousands.

    One could go further than this thesis by: improving our algorithm, providing rigourous bounds on its complexity, or generalizing the algorithm to the n × n × n cube.

     

  • 2961.
    Varagnolo, Damiano
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Schenato, Luca
    Pillonetto, Gianluigi
    A variation of the Newton-Pepys problem and its connections to size-estimation problems2013In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 83, no 5, p. 1472-1478Article in journal (Refereed)
    Abstract [en]

    This paper considers a variation of the 17th century problem commonly known as the Newton-Pepys problem, or the John Smith's problem. We provide its solution and interpret the result in terms of maximum likelihood estimation. In addition, we illustrate the practical relevance of these findings for solving size-estimation problems, and in particular for determining the number of agents in a wireless sensor network.

  • 2962.
    Vasiljeva, Polina
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Combining Unsupervised and Supervised Statistical Learning Methods for Currency Exchange Rate Forecasting2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis we revisit the challenging problem of forecasting currency exchange rate. We combine machine learning methods such as agglomerative hierarchical clustering and random forest to construct a two-step approach for predicting movements in currency exchange prices of the Swedish krona and the US dollar. We use a data set with over 200 predictors comprised of different financial and macro-economic time series and their transformations. We perform forecasting for one week ahead with different parameterizations and find a hit rate of on average 53%, with some of the parameterizations yielding hit rates as high as 60%. However, there is no clear indicator that there exists a combination of the methods and parameters that outperforms all of the tested cases. In addition, our results indicate that the two-step approach is sensitive to changes in the training set.

    This work has been conducted at the Third Swedish National Pension Fund (AP3) and KTH Royal Institute of Technology.

  • 2963.
    Vegi, Nishita
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimization of selecting codeshare flights in aviation2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Airlines are constantly on a look out for partnerships that could facilitate an increase in revenue without having to invest as much. Codesharing is one such solution, where a marketing carrier sells the tickets on another carrier’s flight as its own with its flight number. The codeshares are highly advantageous as they provide new itineraries for the passengers to choose from and increase the traffic for the airline without having to operate the flights.

    The selection of codeshare flights can be time consuming, for the planners, in the absence of tools that help in the decision making. It not only requires a thorough network analysis but the legal and technical constraints to the codeshares have to be considered as well. This thesis aims to perform a research about the different kinds of codeshares and codeshare agreements along with the major decision factors that affect the choice of an airline to choose a codeshare partner.

    The primary purpose of this thesis is to provide a prototype tool that can be developed further and be integrated into the Industrial optimizers’ MP2 software (Multiple purpose/ multiple processing optimization software), a tool used by the transport industry for network planning. The prototype support-tool is designed particularly for the marketing carrier with the devised algorithms which provides a possible method to perform the analysis considering the different options and constraints in regards to the selection of behind and beyond codeshare flights and itineraries.

    The tool processes the available data after which the feasible itineraries are built with respect to the technical, legal and planner specific constraints. To predict the number of passengers who would choose the newly created itineraries, two different models which are based on utility values have been evaluated. The historic passenger choices with the most important factors that affect them are used to create the utility values. The expected passengers and the possible revenues that can be gained from the itineraries then create the base for the final optimization model that suggests the best codeshare flight, along with the expected number of passengers on each itinerary that it is a part of.It should be noted that the revenue management and revenue spilt ups have not been considered in detail for the tool, the most common and simple methods have been considered to perform the analysis, although the different kinds of revenue split ups have been a part of the research, so as to implement them in the MP2 software when required.

  • 2964.
    Vejdemo Johansson, Mikael
    et al.
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. AI Laboratory, Jožef Stefan Institute, Ljubljana, Slovenia .
    Pokorny, Florian T.
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Skraba, Primoz
    Kragic, Danica
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Cohomological learning of periodic motion2015In: Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, E-ISSN 1432-0622, Vol. 26, no 1-2, p. 5-26Article in journal (Refereed)
    Abstract [en]

    This work develops a novel framework which can automatically detect, parameterize and interpolate periodic motion patterns obtained from a motion capture sequence. Using our framework, periodic motions such as walking and running gaits or any motion sequence with periodic structure such as cleaning, dancing etc. can be detected automatically and without manual marking of the period start and end points. Our approach constructs an intrinsic parameterization of the motion and is computationally fast. Using this parameterization, we are able generate prototypical periodic motions. Additionally, we are able to interpolate between various motions, yielding a rich class of 'mixed' periodic actions. Our approach is based on ideas from applied algebraic topology. In particular, we apply a novel persistent cohomology based method for the first time in a graphics application which enables us to recover circular coordinates of motions. We also develop a suitable notion of homotopy which can be used to interpolate between periodic motion patterns. Our framework is directly applicable to the construction of walk cycles for animating character motions with motion graphs or state machine driven animation engines and processed our examples at an average speed of 11.78 frames per second.

  • 2965.
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    A partial A-infinityˆž-structure on the cohomology of C n x C m2008In: Journal of Homotopy & Related Structures (JHRS), ISSN 1512-2891, Vol. 3, no 1, p. 1-11Article in journal (Refereed)
    Abstract [en]

    Suppose k is a finite field, and n, m >= 4 multiples of the field characteristic. Then the A(infinity)-structure of the group cohomology algebras H* (C(n), k) and H* (C(m), k) are well known. We give results characterizing an A(infinity)-structure on H* (C(n) x C(m), k) including limits on non-vanishing low-arity operations and an infinite family of non-vanishing higher operations.

  • 2966.
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Blackbox computation of A-infinityˆž-algebras2010In: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 17, no 2, p. 391-404Article in journal (Refereed)
    Abstract [en]

    Kadeishvili's proof of the minimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231-238] induces an algorithm for the inductive computation of an A(infinity)-algebra structure on the homology of a dg-algebra.In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A(infinity)-algebra structure after a finite amount of computational work.

  • 2967.
    Vejdemo-Johansson, Mikael
    Friedrich-Schiller-Universität Jena, Germany.
    Computation of A-infinity algebras in group cohomology2008Doctoral thesis, monograph (Other academic)
  • 2968.
    Vejdemo-Johansson, Mikael
    Friedrich Schiller University Jena .
    Enumerating the Saneblidze-Umble diagonal in Haskell2008In: ACM Communications in Computer Algebra, ISSN 1932-2240, Vol. 42, no 1-2, p. 20-20Article in journal (Refereed)
    Abstract [en]

    In 2004, Saneblidze and Umble gave a construction of a diagonal on the permutahedron, thus providing important tools to several disciplines using the permutahedra and associated combinatorial polyhedra. There has since been a few, mostly unpublished, attempts at writing computer programs to perform the highly combinatorial construction. The author presents an implementation of the construction in the programming language Haskell: a language which allows one to write computer code that stays very close to the mathematical expression of the construction itself. The author wishes to emphasize the perceived naturality of translating mathematics into Haskell code by giving examples from this program.

  • 2969.
    Vejdemo-Johansson, Mikael
    School of Computer Science, University of St Andrews.
    GAP persistence–a computational topology package for GAP2012Conference paper (Refereed)
    Abstract [en]

    We introduce a recently built package for computing persistent homology within the computer algebra system gap. A native gap implementation of the persistent homology algorithm allows for easier access to the group-theoretic primitives in gap while simultaneously working on computational topology questions – enabling for instance the use of symmetry groups to study symmetric point clouds. The strongest innovation here is in the combination of persistent homology and point cloud algorithms with the group theoretic tools in gap. This package is different from the several existing homological algebra and simplicial topology packages already in gap: simpcomp, homalg, Hap, et c., in that the focus here is on point cloud topology, and not combinatorial complexes or homological algebra.

  • 2970.
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. Jozef Stefan Inst, Slovenia.
    Sketches of a platypus: persistent homology and its algebraic foundations2014In: ALGEBRAIC TOPOLOGY: APPLICATIONS AND NEW DIRECTIONS, American Mathematical Society (AMS), 2014, p. 295-320Conference paper (Refereed)
    Abstract [en]

    The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are rooted in choosing a particular algebraic foundational theory to describe persistent homology, and applying results from that theory to prove useful and important results.

    In this survey paper, we shall examine the various choices in use, and what they allow us to prove. We shall also discuss the inherent differences between the choices people use, and speculate on potential directions of research to resolve these differences.

  • 2971.
    Vejdemo-Johansson, Mikael
    et al.
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Carlsson, Gunnar
    Stanford University.
    Lum, Pek Yee
    Ayasdi Inc..
    Lehman, Alan
    Ayasdi Inc..
    Singh, Gurjeet
    Ayasdi Inc..
    Ishkhanov, Tigran
    Ayasdi Inc..
    The topology of politics: voting connectivity in the US House of Representatives2012Conference paper (Refereed)
    Abstract [en]

    Time-varying topological simplifications of the space of votes in the US House of Representatives (US HoR) display several interesting features unavailable with classical methods of machine learning. In this paper we demonstrate how a re- cently developed topological simplification method, MAPPER, can detect changes in collaboration structures within the US HoR over time.

  • 2972.
    Vejdemo-Johansson, Mikael
    et al.
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Skraba, Primoz
    Jozef Stefan Institute.
    Parallel & scalable zig-zag persistent homology2012Conference paper (Refereed)
    Abstract [en]

    By computing repeated pullbacks, we are able to compute zig-zag persistent homology in a way that easily parallelizes. In this paper, we demonstrate this algorithm together with its underlying mathematical foundation. We can parallelizeand scale the computation scheme.

  • 2973.
    Vignon, Marc
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Implementing Sensitivity Calculations for Long Interest Rate Futures2011Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
  • 2974.
    Vijaykumar, Adithya
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Smoothed Particle Hydrodynamics Simulation for Continuous Casting2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis proposes a way of simulating the continuous casting process of steel using Smoothed Particle Hydrodynamics (SPH). It deals with the SPH modeling of mass, momentum and the energy equations. The interpolation kernel functions required for the SPH modeling of these equations are calculated. Solidification is modeled by some particles are used to represent fluids and others solids. Elastic forces are calculated between the particle neighbors to create deformable bodies. The fluid solidifies into the elastic body when it cools down and the elastic body melts as it is heated. In continuous casting the molten metal solidifies forming a shell when it comes in contact with the cold wall. The mold of the continuous casting is modeled with a cold oscillating wall and a symmetric wall. Once the shell is formed water is sprayed on the solidified metal. If the shell is thin and cooling is not sufficient, the elastic body melts due to the effect of the hot fluid.

  • 2975.
    Viktorsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    The GARCH-copula model for gaugeing time conditional dependence in the risk management of electricity derivatives2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In the risk management of electricity derivatives, time to delivery can be divided into a time grid, with the assumption that within each cell of the grid, volatility is more or less constant. This setup however does not take in to account dependence between the different cells in the time grid.

    This thesis tries to develop a way to gauge the dependence between electricity derivatives at the different places in the time grid and different delivery periods. More specifically, the aim is to estimate the size of the ratio of the quantile of the sum of price changes against the sum of the marginal quantiles of the price changes.

    The approach used is a combination of Generalised Autoregressive Conditional Heteroscedasticity (GARCH) processes and copulas. The GARCH process is used to filter out heteroscedasticity in the price data. Copulas are fitted to the filtered data using pseudo maximum likelihood and the fitted copulas are evaluated using a goodness of fit test.

    GARCH processes alone are found to be insufficient to capture the dynamics of the price data. It is found that combining GARCH with Autoregressive Moving Average processes provides better fit to the data. The resulting dependence is the found to be best captured by elliptical copulas. The estimated ratio is found to be quite small in the cases studied. The use of the ARMA-GARCH filtering gives in general a better fit for copulas when applied to financial data. A time dependency in the dependence can also be observed.

  • 2976.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Adaptive Computation of Aeroacoustic Sources for a Rudimentary Landing Gear2014In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 74, no 6, p. 406-421Article in journal (Refereed)
    Abstract [en]

    We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case, the drag force on the rudimentary landing gear. Turbulent boundary layers are modeled using a simple wall-layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we find good agreement in sound pressure levels, surface velocities, and flow separation. We also compare with detailed surface pressure experimental data where we find largely good agreement, apart from some local differences for which we discuss possible explanations.

  • 2977.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Computation of Aeroacoustic Sources for a Gulfstream G550 Nose Landing Gear Model Using Adaptive FEMManuscript (preprint) (Other academic)
    Abstract [en]

    This work is a direct comparison of our unsteady, turbulent flow simulations with measurements performed using a Gulfstream G550 Nose Landing Gear Model. The experimental campaign, which was carried out by researchers from the NASA Langley Research Center, provided a series of detailed, well documented wind-tunnel measurements for comparison and validation of computational fluid dynamics (CFD) and computational aeroacoustics (CAA) methodologies. Several computational efforts were collected and presented at the Benchmark for Airframe Noise Computation workshops, BANC-I and II. For our simulations, we used a General Galerkin finite element method (G2), where no explicit subgrid model is used, and where the computational mesh is adaptively refined with respect to a posteriori error estimates for a quantity of interest. The mesh is fully unstructured and the solutions are time-resolved, which are key ingredients for solving relevant, industrial applications in the field of aeroacoustics. The comparisons presented here are an attempt to quantify the accuracy of our models, methods and assumptions, and the results, although not perfect, are of relevant quantitative quality. We present several results containing both time-averaged and unsteady flow quantities, always side by side with its corresponding experimental values. The main finding is that we are able to simulate such a complex, unsteady flow problem as the flow past a nose landing gear using a parameter-free methodology for high Reynolds numbers (Re), external aerodynamics and aeroacoustics applications.

  • 2978.
    Villanueva, Walter
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Nuclear Power Safety.
    Boettinger, W.J.
    Metallurgy Division, National Institute of Standards and Technology.
    McFadden, G.B.
    Applied and Computational Mathematics Division, National Institute of Standards and Technology.
    Warren, J.A.
    Metallurgy Division, National Institute of Standards and Technology.
    A diffuse-interface model of reactive wetting with intermetallic formation2012In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 60, no 9, p. 3799-3814Article in journal (Refereed)
    Abstract [en]

    A diffuse-interface model of reactive wetting with intermetallic formation is developed that incorporates fluid flow, phase change and solute diffusion. The model is based on the total molar Gibbs energy of a ternary system with four phases. Numerical simulations were performed using a mesh-adaptive finite element method, revealing the complex behavior of the reactive wetting process. The model was verified against equilibrium states derived from the classical phase diagram and from interface energy considerations. Dynamic results show that the intermetallic can either precede or follow the spreading liquid droplet, depending on the time and the choice of interface energy and kinetic coefficients. Despite this difference, the spreading rate was not affected for the cases considered.

  • 2979.
    Villaume, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Predicting customer level risk patterns in non-life insurance2012Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Several models for predicting future customer profitability early into customer life-cycles in the property and casualty business are constructed and studied. The objective is to model risk at a customer level with input data available early into a private consumer’s lifespan. Two retained models, one using Generalized Linear Model another using a multilayer perceptron, a special form of Artificial Neural Network are evaluated using actual data. Numerical results show that differentiation on estimated future risk is most effective for customers with highest claim frequencies.

     

  • 2980.
    Vinuesa, R.
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, P.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Henningson, D. S.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Characterization of the massively separated wake behind a square cylinder by means of direct numerical simulation2016In: Springer Proceedings in Physics, Springer Science+Business Media B.V., 2016, p. 259-266Conference paper (Refereed)
    Abstract [en]

    The massively separated wake behind a wall-mounted square cylinder is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum thickness Reynolds numbers Reθ ≃ 1000 at the location of the cylinder: one with a fully-turbulent boundary layer as inflow condition, and another one with a laminar boundary layer. The main simulation is performed by using the spectral element code Nek5000. While in the laminar-inflow simulation the horseshoe vortex forming around the cylinder can be observed in the instantaneous flow fields, this is not the case in the turbulent-inflow simulation. Besides, the streaks in the turbulent case become greatly attenuated on both sides of the obstacle. By analyzing the Reynolds shear stress uv, we show that this is due to the modulation of the horseshoe vortex by the turbulence from the incoming boundary layer. © Springer International Publishing Switzerland 2016.

  • 2981.
    Vishe, Pankaj
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A fast algorithm to compute L(1/2, f x chi(q))2013In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 133, no 5, p. 1502-1524Article in journal (Refereed)
    Abstract [en]

    Let f be a fixed (holomorphic or Maass) modular cusp form. Let χq be a Dirichlet character mod q. We describe a fast algorithm that computes the value L(1/2, f × χq) up to any specified precision. In the case when q is smooth or highly composite integer, the time complexity of the algorithm is given by O(1 + |q|5/6 +o(1)).

  • 2982.
    Vishe, Pankaj
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Rapid Computation of L-functions for Modular Forms2013In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, no 11, p. 2624-2656Article in journal (Refereed)
    Abstract [en]

    Let f be a fixed (holomorphic or Maass) modular cusp form, with an L-function L(f,s). We describe an algorithm that computes the value L(f, 1/2 + iT) to any specified precision in time O(1+vertical bar T vertical bar(7/8)).

  • 2983.
    Visontai, Mirko
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Some remarks on the joint distribution of descents and inverse descents2013In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 20, no 1, p. P52-Article in journal (Refereed)
    Abstract [en]

    We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative integer coefficients. We investigate the action of the Eulerian operators that give the recurrence for these generating functions. As a result we devise a recurrence for the coefficients in question but are unable to settle the conjecture. We examine generalizations of the conjecture and obtain a type B analog of the recurrence satisfied by the two-variable generating function. We also exhibit some connections to cyclic descents and cyclic inverse descents. Finally, we propose a combinatorial model for the joint distribution of descents and inverse descents in terms of statistics on inversion sequences.

  • 2984.
    Visontai, Mirko
    et al.
    University of Pennsylvania, United States.
    Williams, Nathan
    Stable multivariate W-Eulerian polynomials2013In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 120, no 7, p. 1929-1945Article in journal (Refereed)
    Abstract [en]

    We prove a multivariate strengthening of Brenti's result that every root of the Eulerian polynomial of type B is real. Our proof combines a refinement of the descent statistic for signed permutations with the notion of real stability a generalization of real-rootedness to polynomials in multiple variables. The key is that our refined multivariate Eulerian polynomials satisfy a recurrence given by a stability-preserving linear operator. Our results extend naturally to colored permutations, and we also give stable generalizations of recent real-rootedness results due to Dilks, Petersen, and Stembridge on affine Eulerian polynomials of types A and C. Finally, although we are not able to settle Brenti's real-rootedness conjecture for Eulerian polynomials of type D. nor prove a companion conjecture of Dilks, Petersen, and Stembridge for affine Eulerian polynomials of types B and D. we indicate some methods of attack and pose some related open problems.

  • 2985.
    Volk, Denis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Almost every interval translation map of three intervals is finite type2014In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 5, p. 2307-2314Article in journal (Refereed)
    Abstract [en]

    Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In this paper, we prove the finiteness conjecture for the ITMs of three intervals. Namely, the subset of ITMs of finite type contains an open, dense, and full Lebesgue measure subset of the space of ITMs of three intervals. For this, we show that any ITM of three intervals can be reduced either to a rotation or to a double rotation.

  • 2986.
    von Feilitzen, Helena
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Modeling non-maturing liabilities2011Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Non‐maturing liabilities, such as savings accounts, lack both predetermined maturity and reset dates due to the fact that the depositor is free to withdraw funds at any time and that the depository institution is free to change the rate. These attributes complicate the risk management of such products and no standardized solution exists. The problem is important however since non‐maturing liabilities typically make up a considerable part of the funding of a bank. In this report different modeling approaches to the risk management are described and a method for managing the interest rate risk is implemented. It is a replicating portfolio approach used to approximate the non‐maturing liabilities with a portfolio of fixed income instruments. The search for a replicating portfolio is formulated as an optimization problem based on regression between the deposit rate and market ratesseparated by a fixed margin. In the report two different optimization criteria are compared for the replicating portfolio, minimizing the standard deviation of the margin versus maximizing the risk‐adjusted margin represented by the Sharpe ratio, of which the latter is found to yield superior results. The choice of historical sample interval over which the portfolio is optimized seems to have a rather big impact on the outcome but recalculating the portfolio weights at regular intervals is found to stabilize the results somewhat. All in all, despite the fact that this type of method cannot fully capture the most advanced dynamics of the non‐maturing liabilities, a replicating portfolio still appears to be a feasible approach for the interest risk management.

  • 2987.
    von Mentzer, Simon
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Risks and scenarios in the Swedish income-based pension system2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this master thesis the risks and scenarios in the Swedish income-based pension system are investigated. To investigate the risks one has chosen to look at a vector autoregressive (VAR) model for three variables (AP-fund returns, average wage returns and inflation). Bootstrap is used to simulate the VAR model. When the simulated values are received they are put back in equations that describes real average wage return, real return from the AP-funds, average wage and income index. Lastly the pension balance is calculated with the simulated data.

    Scenarios are created by changing one variable at the time in the VAR model. Then it is investigated how different scenarios affect the indexation and pension balance.

    The result show a cross correlation structure between average wage return and inflation in the VAR model, but AP-fund returns can simply be modelled as an exogenous white noise random variable. In the scenario when average wage return is altered, one can see the largest changes in indexation and pension balance.

  • 2988.
    von Schwerin, Erik
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    A Stochastic Phase-Field Model Computed From Coarse-Grained Molecular DynamicsManuscript (Other academic)
    Abstract [en]

    Results are presented from numerical experiments aiming at the computation ofstochastic phase-field models for phase transformations by coarse-graining moleculardynamics. The studied phase transformations occur between a solid crystal and aliquid. Nucleation and growth, sometimes dendritic, of crystal grains in a sub-cooledliquid is determined by diffusion and convection of heat, on the macroscopic level,and by interface effects, where the width of the solid–liquid interface is on an atomiclength-scale. Phase-field methods are widely used in the study of the continuum leveltime evolution of the phase transformations; they introduce an order parameter todistinguish between the phases. The dynamics of the order parameter is modelled byan Allen–Cahn equation and coupled to an energy equation, where the latent heat atthe phase transition enters as a source term. Stochastic fluctuations are sometimesadded in the coupled system of partial differential equations to introduce nucleationand to get qualitatively correct behaviour of dendritic side-branching. In this reportthe possibility of computing some of the Allen–Cahn model functions from a microscalemodel is investigated. The microscopic model description of the material bystochastic, Smoluchowski, dynamics is considered given. A local average of contributionsto the potential energy in the micro model is used to determine the local phase,and a stochastic phase-field model is computed by coarse-graining the molecular dynamics.Molecular dynamics simulations on a two phase system at the melting pointare used to compute a double-well reaction term in the Allen–Cahn equation and adiffusion matrix describing the noise in the coarse-grained phase-field.

  • 2989.
    von Schwerin, Erik
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Adaptivity for Stochastic and Partial Differential Equations with Applications to Phase Transformations2007Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    his work is concentrated on efforts to efficiently compute properties of systems, modelled by differential equations, involving multiple scales. Goal oriented adaptivity is the common approach to all the treated problems. Here the goal of a numerical computation is to approximate a functional of the solution to the differential equation and the numerical method is adapted to this task.

    The thesis consists of four papers. The first three papers concern the convergence of adaptive algorithms for numerical solution of differential equations; based on a posteriori expansions of global errors in the sought functional, the discretisations used in a numerical solution of the differential equiation are adaptively refined. The fourth paper uses expansion of the adaptive modelling error to compute a stochastic differential equation for a phase-field by coarse-graining molecular dynamics.

    An adaptive algorithm aims to minimise the number of degrees of freedom to make the error in the functional less than a given tolerance. The number of degrees of freedom provides the convergence rate of the adaptive algorithm as the tolerance tends to zero. Provided that the computational work is proportional to the degrees of freedom this gives an estimate of the efficiency of the algorithm.

    The first paper treats approximation of functionals of solutions to second order elliptic partial differential equations in bounded domains of ℝd, using isoparametric $d$-linear quadrilateral finite elements. For an adaptive algorithm, an error expansion with computable leading order term is derived %. and used in a computable error density, which is proved to converge uniformly as the mesh size tends to zero. For each element an error indicator is defined by the computed error density multiplying the local mesh size to the power of 2+d. The adaptive algorithm is based on successive subdivisions of elements, where it uses the error indicators. It is proved, using the uniform convergence of the error density, that the algorithm either reduces the maximal error indicator with a factor or stops; if it stops, then the error is asymptotically bounded by the tolerance using the optimal number of elements for an adaptive isotropic mesh, up to a problem independent factor. Here the optimal number of elements is proportional to the d/2 power of the Ldd+2

    quasi-norm of the error density, whereas a uniform mesh requires a number of elements proportional to the d/2 power of the larger L1 norm of the same error density to obtain the same accuracy. For problems with multiple scales, in particular, these convergence rates may differ much, even though the convergence order may be the same.

    The second paper presents an adaptive algorithm for Monte Carlo Euler approximation of the expected value E[g(X(τ),\τ)] of a given function g depending on the solution X of an \Ito\ stochastic differential equation and on the first exit time τ from a given domain. An error expansion with computable leading order term for the approximation of E[g(X(T))] with a fixed final time T>0 was given in~[Szepessy, Tempone, and Zouraris, Comm. Pure and Appl. Math., 54, 1169-1214, 2001]. This error expansion is now extended to the case with stopped diffusion. In the extension conditional probabilities are used to estimate the first exit time error, and difference quotients are used to approximate the initial data of the dual solutions. For the stopped diffusion problem the time discretisation error is of order N-1/2 for a method with N uniform time steps. Numerical results show that the adaptive algorithm improves the time discretisation error to the order N-1, with N adaptive time steps.

    The third paper gives an overview of the application of the adaptive algorithm in the first two papers to ordinary, stochastic, and partial differential equation. The fourth paper investigates the possibility of computing some of the model functions in an Allen--Cahn type phase-field equation from a microscale model, where the material is described by stochastic, Smoluchowski, molecular dynamics. A local average of contributions to the potential energy in the micro model is used to determine the local phase, and a stochastic phase-field model is computed by coarse-graining the molecular dynamics. Molecular dynamics simulations on a two phase system at the melting point are used to compute a double-well reaction term in the Allen--Cahn equation and a diffusion matrix describing the noise in the coarse-grained phase-field.

  • 2990.
    von Schwerin, Erik
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Convergence rates of adaptive algorithms for stochastic and partial differential equations2005Licentiate thesis, comprehensive summary (Other scientific)
  • 2991. von Schwerin, Erik
    et al.
    Szepessy, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A stochastic phase-field model determined from molecular dynamics2010In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 44, no 4, p. 627-646Article in journal (Refereed)
    Abstract [en]

    The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average.

  • 2992. von Sydow, Lina
    et al.
    Ghafari, Paria
    Lehto, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. Uppsala University, Sweden.
    Wangersjo, Mats
    Pricing of Basket Options Using Dimension Reduction and Adaptive Finite Differences in Space, and Discontinuous Galerkin in Time2016In: NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS (ENUMATH 2015) / [ed] Karasozen, B Manguoglu, M TezerSezgin, M Goktepe, S Ugur, O, SPRINGER INT PUBLISHING AG , 2016, p. 607-615Conference paper (Refereed)
    Abstract [en]

    European basket options are priced by solving the multi-dimensional Black-Scholes-Merton equation. Standard numerical methods to solve these problems often suffer from the "curse of dimensionality". We tackle this by using a dimension reduction technique based on a principal component analysis with an asymptotic expansion. Adaptive finite differences are used for the spatial discretization. In time we employ a discontinuous Galerkin scheme. The efficiency of our proposed method to solve a five-dimensional problem is demonstrated through numerical experiments and compared with a Monte-Carlo method.

  • 2993.
    Vorwerk, Kathrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Connectivity and embeddability of buildings and manifolds2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The results presented in is thesis concern combinatorial and topological properties of objects closely related to geometry, but regarded in combinatorial terms. Papers A and C have in common that they are intended to study properties of buildings, whereas Papers A and B both are concerned with the connectivity of graphs of simplicial complexes.

    In Paper A it is shown that graphs of thick, locally finite and 2-spherical buildings have the highest possible connectivity given their regularity and maximal degree. Lower bounds on the connectivity are given also for graphs of order complexes of geometric lattices.

    In Paper B an interpolation between two classical results on the connectivity of graphs of combinatorial manifolds is developed. The classical results are by Barnette for general combinatorial manifolds and by Athanasiadis for flag combinatorial manifolds. An invariant b Δof a combinatorial manifold Δ is introduced and it is shown thatthe graph of is (2dbΔ)-connected. The concept of banner triangulations of manifolds is defined. This is a generalization of flagtriangulations, preserving Athanasiadis’ connectivity bound.

    In Paper C we study non-embeddability for order complexes of thick geometric lattices and some classes of finite buildings, all of which are d-dimensional order complexes of certain posets. They are shown to be hard to embed, which means that they cannot be embedded in Eucledian space of lower dimension than 2d+1, which is sufficient for all d-dimensional simplicial complexes. The notion of weakly independent atom configurations in general posets is introduced. Using properties of the van Kampen obstruction, it is shown that the existence of such a configuration makes the order complex of a poset hard to embed.

  • 2994.
    Vu, Tam
    KTH, School of Education and Communication in Engineering Science (ECE).
    Då som nu för alltid: Att skriva ett kompendium till gymnasielärare med förslag för hur matematikens historia kan integreras i matematikundervisningen2016Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This master thesis deals with the use of the history of mathematics in teaching mathematics in Swedish gymnasium schools. A "gymnasium" in Sweden (not to be confused with a gymnastics school) is a type of school which consists of three years, after nine years of elementary school. The main focus of this thesis is to investigate how mathematics teachers can integrate historical aspects of mathematics into their classes, and to give concrete examples of such integration. This thesis illustrates, above all, an integration of mathematics history with problem solving, where problems are selected so that they are relevant to the syllabus and can be connected to important mathematicians in history as well as how mathematics itself has evolved through the ages.

    The questions to be answered in this thesis concern which mathematical problems that may serve as a basis for discussion in the classroom and how teachers may illuminate the historical connections contained in each discussed problem. The proposed problems and connections are compiled in a compendium which is meant to be read by mathematics teachers teaching at gymnasiums.

    The methods which have been used to produce the compendium are partly literature study of earlier works about mathematics and mathematics didactics in relation to mathematical history, partly qualitative interviews with experienced mathematics teachers at gymnasiums. The interviewed teachers read selected parts of the prototypal compendium and gave opinions and suggestions of improvement so that the final compendium would work well for the meant target group.

    Despite the fact that the compendium is not a textbook, a certain pedagogical quality is to be attained. The compendium should convey the history of mathematics in a clear and concise manner, where the involved mathematical problems and historical connections should be experienced as interesting and meaningful for mathematics teachers.

  • 2995. Vynnycky, M.
    et al.
    Shugai, Galina
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Yakubenko, P.
    Mellgren, Niklas
    KTH, School of Engineering Sciences (SCI), Mechanics.
    ASYMPTOTIC REDUCTION FOR NUMERICAL MODELING OF POLYMER ELECTROLYTE FUEL CELLS2009In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 70, no 2, p. 455-487Article in journal (Refereed)
    Abstract [en]

    Most existing three-dimensional (3D) models for the polymer electrolyte fuel cell (PEFC), as well as other types of fuel cells, are fully numerical and computationally expensive. While such models are undoubtedly useful, they cannot provide the qualitative understanding that comes from a complete prior nondimensional analysis of the problem. Here, earlier ideas for the derivation of a two-dimensional (2D) asymptotically reduced model to describe steady isothermal gas-phase flow in the cathode of a PEFC are extended to a 3D nonisothermal model for a whole PEFC with straight channel flow distributors. As well as providing characteristic current density and temperature difference scales for the whole cell, it is also possible to extract potential drops over individual cell components. The analysis indicates that, for realistic operating ranges, the PEFC is sufficiently isothermal with respect to the mass, momentum, and charge transport to enable the thermal problem to be decoupled from the rest, a simplification not noted previously. After the relevant nondimensional parameters have been identified, a reduced model is proposed and some preliminary numerical results comparing the polarization curves obtained from the reduced and 3D models are presented. Good agreement is found; most significantly, the reduced model is found to require between one and two orders of CPU time less than the full 3D model.

  • 2996.
    Vynnycky, Michael
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland.
    An asymptotic model for the primary drying stage of vial lyophilization2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 96, no 1, p. 175-200Article in journal (Refereed)
    Abstract [en]

    Asymptotic methods are employed to analyse a commonly used one-dimensional transient model for coupled heat and mass transfer in the primary drying stage of freeze-drying (lyophilization) in a vial. Mathematically, the problem constitutes a two-phase moving boundary problem, in which one of the phases is a frozen porous matrix that undergoes sublimation, and the other is a low-pressure binary gaseous mixture. Nondimensionalization yields a model with 19 dimensionless parameters, but a systematic separation of timescales leads to a reduced model consisting of just a second-order differential equation with two initial conditions for the location of a sublimation front; the temperature and gas partial pressures can be found a posteriori. The results of this asymptotic model are compared with those of earlier experimental and theoretical work. Most significantly, the current model would be a computationally efficient tool for predicting the onset of secondary drying.

  • 2997.
    Vynnycky, Michael
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland .
    Gordon, A. D.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland .
    Non-isothermal hydrophobicity-dependent two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell2015In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 92, no 1, p. 123-146Article in journal (Refereed)
    Abstract [en]

    In this paper, we extend a recent one-dimensional isothermal steady-state generalized Darcy model for two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell, so as to include the effect of heat transfer. As for the isothermal case, we arrive at either a fixed- or free-boundary problem, depending on the main problem parameters: inlet temperature (), inlet water saturation (), inlet relative humidity (RH), porous medium hydrophobicity and cathode overpotential (). The inclusion of heat transfer is found to limit the range of values of and RH over which two-phase flow can occur, as compared to that predicted by the isothermal model. The ensuing non-isothermal two-phase flow model equations are then computed numerically, with particular care being required for the treatment of an integrably singular inter-phase mass transfer term.

  • 2998.
    Vynnycky, Michael
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland .
    Kanev, K.
    Mathematical Analysis of the Multisolution Phenomenon in the P3P Problem2015In: Journal of Mathematical Imaging and Vision, ISSN 0924-9907, E-ISSN 1573-7683, Vol. 51, no 2, p. 326-337Article in journal (Refereed)
    Abstract [en]

    The perspective 3-point problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis and robotics. One line of activity involves formulating it mathematically in terms of finding the solution to a quartic equation. However, in general, the equation does not have a unique solution, and in some situations there are no solutions at all. Here, we present a new approach to the solution of the problem; this involves closer scrutiny of the coefficients of the polynomial, in order to understand how many solutions there will be for a given set of problem parameters. We find that, if the control points are equally spaced, there are four positive solutions to the problem at 25 % of all available spatial locations for the control-point combinations, and two positive solutions at the remaining 75 %.

  • 2999.
    Vynnycky, Michael
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals.
    Mitchell, S. L.
    On the numerical solution of a Stefan problem with finite extinction time2015In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 276, p. 98-109Article in journal (Refereed)
    Abstract [en]

    In many phase-change problems of practical interest, it is important to know when a phase is depleted, a quantity referred to as the extinction time; however, there are no numerical schemes that are able to compute this with any degree of rigour or formal accuracy. In this paper, we develop such a scheme for the one-dimensional time-dependent problem of an evaporating spherical droplet. The Keller box finite-difference scheme is used, in tandem with the so-called boundary immobilization method. An important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space, in particular as regards resolving a square-root singularity in the droplet radius as the extinction time is approached.

  • 3000.
    Vynnycky, Michael
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Saleem, Saud
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals.
    Fredriksson, Hasse
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals.
    An asymptotic approach to solidification shrinkage-induced macrosegregation in the continuous casting of binary alloys2018In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 54, p. 605-626Article in journal (Refereed)
    Abstract [en]

    The modelling of macrosegregation in the continuous casting of alloys normally requires resource-intensive computational fluid dynamics (CFD). By contrast, here we develop an asymptotic framework for the case when macrosegregation is driven by solidification shrinkage; as a first step, a binary alloy is considered. Systematic asymptotic analysis of the steady-state two-dimensional mass, momentum, heat and solute conservation equations in terms of the shrinkage parameter indicates that the overall problem can be reduced to a hierarchy of decoupled problems: a leading-order problem that is non-linear, and a sequence of linear problems, with the actual macrosegregation of the solute then being determined by means of one-dimensional quadrature. A numerical method that solves this sequence is then developed and implemented, and yields realistic macrosegregation profiles at low computational cost.

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