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  • 2951.
    Strömqvist, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Koroleva, Yulia
    Lomonosov Moscow State University.
    Gamma-convergence of Oscillating Thin Obstacles2013In: Eurasian Mathematical Journal, ISSN 2077-9879, Vol. 4, p. 88-100Article in journal (Refereed)
  • 2952.
    Styrud, Lovisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    PÅVERKAS DEN KOMMUNALA SKATTESATSEN AV POLITISKT STYRE?: En strukturell analys av faktorer som avgör skatten i svenska kommuner2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of this report was to investigate which factors determine municipal taxes in Sweden.The aim was also to find out whether and how the forms of political rule are significant covariates. A multiple regression analysis was performed using data from 289 municipalities. The analysis resulted in five dierent models, of which a model based on municipal grouping was found to be most satisfactory. In all of the models, there are effects from the form of political rule. The results indicate that socialist municipalities have higher tax rates than non-socialist. Also, coalitions between socialist and non-socialist parties have higher taxr ates than purely non-socialist rules. Finally, majority rules have higher tax rates compared to minorities.

  • 2953.
    Styrud, Lovisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Risk Premium Prediction of Car Damage Insurance using Artificial Neural Networks and Generalized Linear Models2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Over the last few years the interest in statistical learning methods, in particular artificial neural networks, has reawakened due to increasing computing capacity, available data and a strive towards automatization of different tasks. Artificial neural networks have numerous applications, why they appear in various contexts. Using artificial neural networks in insurance rate making is an area in which a few pioneering studies have been conducted, with promising results. This thesis suggests using a multilayer perceptron neural network for pricing car damage insurance. The MLP is compared with two traditionally used methods within the framework of generalized linear models. The MLP was selected by cross-validation of a set of candidate models. For the comparison models, a log-link GLM with Tweedie's compound Poisson distribution modeling the risk premium as dependent variable was set up, as well as a two-parted GLM with a log-link Poisson GLM for claim frequency and a log-link Gamma GLM for claim severity. Predictions on an independent test set showed that the Tweedie GLM had the lowest prediction error, followed by the MLP model and last the Poisson-Gamma GLM. Analysis of risk ratios for the different explanatory variables showed that the Tweedie GLM was also the least discriminatory model, followed by the Poisson-Gamma GLM and the MLP. The MLP had the highest bootstrap estimate of variance in prediction error on the test set. Overall however, the MLP model performed roughly in line with the GLM models and given the basic model configurations cross-validated and the restricted computing power, the MLP results should be seen as successful for the use of artificial neural networks in car damage insurance rate making. Nevertheless, practical aspects argue in favor of using GLM.

    This thesis is written at If P&C Insurance, a property and casualty insurance company active in Scandinavia, Finland and the Baltic countries. The headquarters are situated in Bergshamra, Stockholm.

  • 2954.
    Stålnacke, Emil
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Parameter study of a muffle furnace performance on powder heating using numerical multiphysics simulation with COMSOL2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The muffle furnace main purpose is to anneal the rough sponge iron powder transported through it, which is done by burning natural gas. Heat is absorbed by the muffle and is transferred to the bed of sponge iron powder. In order to reduce the consumptions of fossil fuel, some companies of the industry aims to exchange the natural gas in their muffle furnace’s burners to syngas, produced from biomass. This will however affect the performance of the furnace in the heating aspect. For this work, it is assumed that the effect will be negative. Thus the aim of this study is to investigate how to compensate the loss of effect from the burners, by examining which other parameters have influence on the furnace heating performance of the sponge iron powder transported through the furnace. The investigation is executed by simulating a 1 meter of the furnace in COMSOL multiphysics for 10 min, not including the combustion chambers. The investigated parameters are the packing degree of the powder, surface emissivity of the muffle, process gas velocity, conveyor belt velocity and the heat transfer rate coefficient to muffle from the combustion chambers. Alas, the process gas velocity and conveyor belt velocity only have minor influence on the final result, according to this simulation. However, the simulation exhibited that the surface emissivity of the muffle and the packing degree of the powder has great impact on the heating of the powder and could compensate some of the lost effect from the burners. This could be obtained by using an unpolished and oxidized muffle surface, and use densely packed powder sample.

  • 2955.
    Su, Xun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Cheung, Mei Ting
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Day-of-the-week eects in stock market data2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of this thesis is to investigate day-of-the-week effects for stock index returns. The investigations include analysis of means and variances as well as return-distribution properties such as skewness and tail behavior. Moreover, the existences of conditional day-of-the-week effects, depending on the outcome of returns from the previous week, are analyzed. Particular emphasis is put on determining useful testing procedures for differences in variance in return data from different weekdays. Two time series models, AR and GARCH(1,1), are used to find out if any weekday's mean return is different from other days. The investigations are repeated for two-day re- turns and for returns of diversified portfolios made up of several stock index returns.

  • 2956.
    Sudhakar, Yogaraj
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Technical University of Munich, Germany.
    Sommariva, Alvise
    Vianello, Marco
    Wall, Wolfgang A.
    On the use of compressed polyhedral quadrature formulas in embedded interface methods2017In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, no 3, p. B571-B587Article in journal (Refereed)
    Abstract [en]

    The main idea of this paper is to apply a recent quadrature compression technique to algebraic quadrature formulas on complex polyhedra. The quadrature compression substantially reduces the number of integration points but preserves the accuracy of integration. The compression is easy to achieve since it is entirely based on the fundamental methods of numerical linear algebra. The resulting compressed formulas are applied in an embedded interface method to integrate the weak form of the Navier-Stokes equations. Simulations of flow past stationary and moving interface problems demonstrate that the compressed quadratures preserve accuracy and rate of convergence and improve the efficiency of performing the weak form integration, while preserving accuracy and order of convergence.

  • 2957.
    Sun, Yi
    et al.
    Courant Institute of Mathematical Sciences, New York University, New York, USA.
    Caflisch, Russel
    Department of Mathematics, California NanoSystem Institute and Institute for Pure and Applied.
    Engquist, Björn
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    A multiscale method for epitaxial growth2011In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 9, no 1, p. 335-354Article in journal (Refereed)
    Abstract [en]

    In this paper we investigate a heterogeneous multiscale method (HMM) for interface tracking and apply the technique to the simulation of epitaxial growth. HMM relies on an efficient coupling between macroscale and microscale models. When the macroscale model is not fully known explicitly or not accurate enough, HMM provides a procedure for supplementing the missing data from a microscale model. Here we design a multiscale method that couples kinetic Monte-Carlo (KMC) simulations on the microscale with the island dynamics model based on the level set method and a diffusion equation. We perform the numerical simulations for submonolayer island growth and step edge evolutions on the macroscale domain while keeping the KMC modeling of the internal boundary conditions. Our goal is to get comparably accurate solutions at potentially lower computational cost than for the full KMC simulations, especially for the step flow problem without nucleation.

  • 2958.
    Sundberg, Jesper
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Anomaly Detection in Diagnostics Data with Natural Fluctuations2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis, the red hot topic anomaly detection is studied, which is a subtopic in machine learning. The company, Procera Networks, supports several broadband companies with IT-solutions and would like to detected errors in these systems automatically. This thesis investigates and devises methods and algorithms for detecting interesting events in diagnostics data. Events of interest include: short-term deviations (a deviating point), long-term deviations (a distinct trend) and other unexpected deviations. Three models are analyzed, namely Linear Predictive Coding, Sparse Linear Prediction and Wavelet Transformation. The final outcome is determined by the gap to certain thresholds. These thresholds are customized to fit the model as well as possible.

  • 2959.
    Sundberg, Victor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Application and Bootstrapping of the Munich Chain Ladder Method2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Point estimates of the Standard Chain Ladder method (CLM) and of the more complex Munich Chain Ladder method (MCL) are compared to real data on 38 different datasets in order to evaluate if MCL produces better predictions on average with a dataset from an arbitrary insurance portfolio. MCL is also examined to determine if the future paid and incurred claims converge as time progresses. A bootstrap model based on MCL (BMCL) is examined in order to evaluate its possibility to estimate the probability density function (PDF) of future claims and observable claim development results (OCDR). The results show that the paid and incurred predictions by MCL converge. The results also show that when considering all datasets MCL produce on average better estimations than CLM with paid data but no improvement can be seen with incurred data. Further the results show that by considering a subset of datasets which fulfil certain criteria, or by only considering accident years after 1999 the percentage of datasets in which MCL produce superior estimations increases. When examining BMCL one finds that it can produce estimated PDFs of ultimate reserves and OCDRs, however the mean of estimate of ultimate reserves does not converge to the MCL estimates nor do the mean of the OCDRs converge to zero. In order to get the right convergence the estimated OCDR PDFs are centered and the mean of the BMCL estimated ultimate reserve is set to the MCL estimate by multiplication.

  • 2960.
    Sundin, Jesper
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Risk contribution and its application in asset and risk management for life insurance2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In risk management one important aspect is the allocation of total portfolio risk into its components. This can be done by measuring each components' risk contribution relative to the total risk, taking into account the covariance between components. The measurement procedure is straightforward under assumptions of elliptical distributions but not under the commonly used multivariate log-normal distributions. Two portfolio strategies are considered, the "buy and hold" and the "constant mix" strategy. The profits and losses of the components of a generic portfolio strategy are defined in order to enable a proper definition of risk contribution for the constant mix strategy. Then kernel estimation of risk contribution is performed for both portfolio strategies using Monte Carlo simulation. Further, applications for asset and risk management with risk contributions are discussed in the context of life insurance.

  • 2961.
    Sundqvist, Greger
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Model risk in a hedging perspective2011Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
  • 2962.
    Sundström, Dennis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Automatized GARCH parameter estimation2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This paper is about automatizing parameter estimation of GARCH type conditional volatility models for the sake of using it in an automated risk monitoring system. Many challenges arise with this task such as guaranteeing convergence, being able to yield reasonable results regardless of the quality of the data, accuracy versus speed of the algorithm to name a few. These problems are investigated and a robust framework for an algorithm is proposed, containing dimension reducing and constraint relaxing parameter space transformations with robust initial values. The algorithm is implemented in java with two models, namely the GARCH and gjr-GARCH model. By using real market data, performance of the algorithm are tested with various in-sample and out-of-sample measures, including backtesting of the widely used risk measure Value-at-Risk. The empirical studies conclude that the more complex gjr-sGARCH model with the conditional student’s t distribution was found to yield the most accurate results. However for the purpose of this paper the GARCH orgjr-GARCH seems more appropriate.

  • 2963.
    Suzuki, Toshihiro
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A Game Theoretic Approach to Multi-Agent Cooperation with Application to Economic Systems2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Consensus problem with multi-agent systems has interested researchers in various areas. Its difficulties tend to appear when available information of each agent is limited for achieving consensus. Besides, it is not always the case that agents can catch the whole states of the others; an output is often the only possible measurement for each agent in applications. The idea of graph Laplacian is then of help to address such a troublesome situation. While every single agent obviously makes decision to achieve an individual goal of minimizing its own cost functional, all agents as a team can obtain even more improvement by cooperation in some cases, which leads to cooperative game theoretic approach. The main goal of this master thesis is to accomplish a combination of optimal control theory and cooperative game theory in order to solve the output consensus problem with limited network connectivity. Along with this combination, bargaining problems are considered out of necessity.

     

  • 2964.
    Suzuki, Yuya
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Rare-event Simulation with Markov Chain Monte Carlo2013Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this thesis, we consider random sums with heavy-tailed increments. By the term random sum, we mean a sum of random variables where the number of summands is also random. Our interest is to analyse the tail behaviour of random sums and to construct an efficient method to calculate quantiles. For the sake of efficiency, we simulate rare-events (tail-events) using a Markov chain Monte Carlo (MCMC) method. The asymptotic behaviour of sum and the maximum of heavy-tailed random sums is identical. Therefore we compare random sum and maximum value for various distributions, to investigate from which point one can use the asymptotic approximation. Furthermore, we propose a new method to estimate quantiles and the estimator is shown to be efficient.

  • 2965.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Svärd, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Density filters for topology optimization based on the Pythagorean means2013In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 48, no 5, p. 859-875Article in journal (Refereed)
    Abstract [en]

    In topology optimization, restriction methods are needed to prohibit mesh dependent solutions and enforce length scale on the optimized structure. This paper presents new restriction methods in the form of density filters. The proposed filters are based on the geometric and harmonic means, respectively, and possess properties that could be of interest in topology optimization, for example the possibility to obtain solutions which are almost completely black and white. The article presents the new filters in detail, and several numerical test examples are used to investigate the properties of the new filters compared to filters existing in the literature. The results show that the new filters in several cases provide solutions with competitive objective function values using few iterations, but also, and perhaps more importantly, in many cases, different filters make the optimization converge to different solutions with close to equal value. A variety of filters to choose from will hence provide the user with several suggested optimized structures, and the new filters proposed in this work may certainly provide interesting alternatives.

  • 2966.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A hierarchical neighbourhood search method for topology optimization2005In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 29, no 5, p. 325-340Article in journal (Refereed)
    Abstract [en]

    This paper presents a hierarchical neighbourhood search method for solving topology optimization problems defined on discretized linearly elastic continuum structures. The design of the structure is represented by binary design variables indicating material or void in the various finite elements.

    Two different designs are called neighbours if they differ in only one single element, in which one of them has material while the other has void. The proposed neighbourhood search method repeatedly jumps to the "best" neighbour of the current design until a local optimum has been found, where no further improvement can be made. The "engine" of the method is an efficient exploitation of the fact that if only one element is changed (from material to void or from void to material) then the new global stiffness matrix is just a low-rank modification of the old one. To further speed up the process, the method is implemented in a hierarchical way. Starting from a coarse finite element mesh, the neighbourhood search is repeatedly applied on finer and finer meshes.

    Numerical results are presented for minimum-weight problems with constraints on respectively compliance, strain energy densities in all non-void elements, and von Mises stresses in all non-void elements.

  • 2967.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the validity of using small positive lower bounds on design variables in discrete topology optimization2009In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 37, no 4, p. 325-334Article in journal (Refereed)
    Abstract [en]

    It is proved that an optimal {epsilon, 1}(n) solution to a "epsilon-perturbed" discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to {0, 1}(n), to the corresponding "unperturbed" discrete problem, provided that the constraints in the perturbed problem are carefully defined and epsilon > 0 is sufficiently small.

  • 2968.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sequential integer programming methods for stress constrained topology optimization2007In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 34, no 4, p. 277-299Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of load carrying structures defined on a discretized design domain where binary design variables are used to indicate material or void in the various finite elements. The main contribution is the development of two iterative methods which are guaranteed to find a local optimum with respect to a 1-neighbourhood. Each new iteration point is obtained as the optimal solution to an integer linear programming problem which is an approximation of the original problem at the previous iteration point. The proposed methods are quite general and can be applied to a variety of topology optimization problems defined by 0-1 design variables. Most of the presented numerical examples are devoted to problems involving stresses which can be handled in a natural way since the design variables are kept binary in the subproblems.

  • 2969.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Topology optimization by a neighbourhood search method based on efficient sensitivity calculations2006In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 67, no 12, p. 1670-1699Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of discretized load-carrying continuum structures, where the design of the structure is represented by binary design variables indicating material or void in the various finite elements. Efficient exact methods for discrete sensitivity calculations are developed. They utilize the fact that if just one or two binary variables are changed to their opposite binary values then the new stiffness matrix is essentially just a low-rank modification of the old stiffness matrix, even if some nodes in the structure may disappear or re-enter. As an application of these efficient sensitivity calculations, a new neighbourhood search method is presented, implemented, and applied on some test problems, one of them with 6912 nine-node finite elements where the von Mises stress in each non-void element is considered.

  • 2970.
    Svedberg, Christopher
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Future stability of the Einstein-Maxwell-Scalar field system and non-linear wave equations coupled to generalized massive-massless Vlasov equations2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of two articles related to mathematical relativity theory.

    In the first article we prove future stability of certain spatially homogeneous solutionsto Einstein’s field equations. The matter model is assumed to consist of an electromagnetic field and a scalar field with a potential creating an accelerated expansion. Beside this, more general properties concerning Einstein’s field equation coupled to a scalar field and an electromagnetic field are settled. The most important of these questions are the existence of a maximal globally hyperbolic development and the Cauchy stability of solutions to the initial value problem.

    In the second article we consider Einstein’s field equations where the matter model consists of two momentum distribution functions. The first momentum distribution function represents massive matter, for instance galactic dust, and the second represents massless matter, for instance radiation. Furthermore, we require that each of the momentum distribution functions shall satisfy the Vlasov equation. This means that the momentum distribution functions represent collisionless matter. If Einstein’s field equations with such a matter model is expressed in coordinates and if certain gauges are fixed we get a system of integro-partial differential equations we shall call non-linear wave equations coupled to generalized massive-massless Vlasov equations. In the second article we prove that the initial value problem associated to this kind of equations has a unique local solution.

  • 2971.
    Svedberg, Christopher
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Non-linear wave equations coupled to generalized massive-massless Vlasov equationsManuscript (preprint) (Other academic)
    Abstract [en]

    Consider Einstein’s field equations where the matter model consists oftwo momentum distribution functions. Let the first momentum distribution function represent massive matter, for instance galactic dust, and let the second represent massless matter, for instance radiation. Furthermore,let us require that each of the momentum distribution functions shall satisfy the Vlasov equation. This means that the momentum distribution functions represent collisionless matter. If Einstein’s field equations withsuch a matter model is expressed in coordinates and if certain gauges arefixed we get a system of integro-partial differential equations we shall call non-linear wave equations coupled to generalized massive-massless Vlasovequations. We prove that the initial value problem associated to this kindof equations has a unique local solution. Moreover, we prove a continuation criterion for the solution.

  • 2972.
    Svedberg, Victoria
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Development of a test bench for Gamma Knife Optimization2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The dose distribution in the Gamma Knife (developed and produced by Elekta) is optimized over the weights (or Beam-on time) using different models other than the radiosurgical one used in Leksell Gamma Plan . These are based on DVH, EUD, TCP and NTCP. Also adding hypoxic regions are tested in the Gamma Knife to see whether or not the dose can be guided to these areas. This is done in two ways. For the DVH and EUD model the hypoxic area is regarded as a organ by itself and higher constraints is defined on it. In the TCP case blood vessels are outlined and the α and β parameters are perturbed to describe a hypoxic area. The models are tested in two cases. The first one is one tumour close to the brainstem and the second case is two tumours located far away from each other. Finally the results are compared to the dose distribution computed by the Gamma Knife.

     

  • 2973.
    Svedin, Maria
    et al.
    KTH, School of Computer Science and Communication (CSC), Media Technology and Interaction Design, MID. KTH, School of Education and Communication in Engineering Science (ECE). Stockholm University.
    Bälter, Olle
    KTH, School of Computer Science and Communication (CSC), Media Technology and Interaction Design, MID. KTH, School of Education and Communication in Engineering Science (ECE).
    Pettersson, Kerstin
    Stockholm University.
    Scheja, Max
    Stockholm University.
    ASSIST as a tool to evaluate course design2012In: Learners in the Driving Seat. Users? - Partners? - Consumers? - Peers? Where are we heading to?: Book of Abstracts / [ed] Morten Flate Paulsen & András Szúcs, 2012, p. 110-111Conference paper (Refereed)
    Abstract [en]

    In order to analyse the course design in two online preparatory university courses in mathematics and programming, a Swedish translation of the short version of the Approaches and Study Skills Inventory for Students (ASSIST) was distributed. Four hundred and ninety three students, representing 24 % response rate, participated. The result showed that the mathematics course discouraged students who adopt a deep/strategic approach, while the programming course discouraged students with a deep approach and encouraged students with a surface approach. The indications differences in course design in two online preparatory university courses in mathematics and programming, a Swedish translation of the short version of the Approaches and Study Skills Inventory for Students (ASSIST) was distributed to the students participating. The result showed that the mathematics course discouraged students who adopt a deep/strategic approach, while the programming course discouraged students with a deep approach and encouraged students with a surface approach. The indications may beare a contribution to the discussion on disciplinary differences in approaches to studying as well as in disposition of online courses.

  • 2974.
    Svensson, David
    KTH, School of Education and Communication in Engineering Science (ECE).
    Studera och diskutera lösningsförslag: En studie om gymnasieelevers utveckling av begreppsförmåga och procedurförmåga2015Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Recent research indicate that learning from worked examples might be superior for novice learners compared to solving traditional math problems without solutions. Learners who also actively process the information in the presented example seem to profit noticeably from this learning mode. These reoccurring findings are now referred to as the "worked example effect". Cognitive load theorists argues that solving conventional problems imposes an extraneous cognitive load that interferers with learning, while worked examples reduces extraneous load which free working memory for germane cognitive activities beneficial for learning.

    The reason for this study is to examine how the uses of worked examples, in normal teacher-lead classroom conditions, affects conceptual- and procedural-skill acquisition in mathematics, compared to traditional teacher-lead education in Sweden. This is done by comparing the result of 76 tests done by students having traditional education with 76 similar tests done by students having used an educational method called SDL, which involves studying and discussing worked examples. The students are considered as novice within the studied area and the performance measured involves both imitative and creative reasoning. Although earlier studies indicate a superiority of different worked example approaches, no significant difference in skill acquisition between the groups where found in this study. Hence, this study questions the hypothesis that teacher- lead worked examples activities would be superior to traditional educational methods. Studying worked examples might be an effective learning method, when no other guidance is available. In traditional classroom education, guidance can also be given from teachers, which might explain the similar learning outcomes found in this study.

  • 2975.
    Svensson Depraetere, Xavier
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Application of new particle-based solutions to the Simultaneous Localization and Mapping (SLAM) problem2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

        In this thesis, we explore novel solutions to the Simultaneous Localization and Mapping (SLAM) problem based on particle filtering and smoothing methods. In essence, the SLAM problem constitutes of two interdependent tasks: map building and tracking. Three solution methods utilizing different smoothing techniques are explored. The smoothing methods used are fixed lag smoothing (FLS), forward-only forward-filtering backward-smoothing (forward-only FFBSm) and the particle-based, rapid incremental smoother (PaRIS). In conjunction with these smoothing techniques the well-established Expectation-Maximization (EM) algorithm is used to produce maximum-likelihood estimates of the map. The three solution method are then evaluated and compared in a simulated setting.

  • 2976.
    Svensson, Jenni
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Multiobjective optimization in radiosurgery: How to approximate and navigate on the Pareto surface2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Cancer is a common cause of death worldwide and radiotherapy is one of the treatments used. Since treatment planning is a time consuming matter for the radiation therapist, a way to decrease the time spent finding the plan would be an improvement. This can be achieved by precalculating a number of optimal plans and then choosing among these in real-time.

    In this thesis a dual algorithm for approximation of the Pareto optimal plans suggested by Bokrantz and Forsgren, was adapted to the parameters of the Leksell Gamma Knife®. A Graphical User Interface was also created, based on the navigation tool described by Monz et al to enable choosing among the pre-calculated dose plans.

    The computational time of the algorithm was investigated and the dimensionality of the solutions and Pareto optimal points were looked at to see if it might be possible to reduce the number of dimensions to speed up computations.

    Although no certain conclusions can be drawn about dimensionality reduction, I found no reason to rule that possibility out. It was also confirmed that there is reason to keep the number of objectives low to get a better approximation.

     

  • 2977.
    Svensson, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On Importance Sampling and Dependence Modeling2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of four papers.

    In the first paper, Monte Carlo simulation for tail probabilities of heavy-tailed random walks is considered. Importance sampling algorithms are constructed by using mixtures of the original distribution with some other state-dependent distributions. Sufficient conditions under which the relative error of such algorithms is bounded are found, and the bound is calculated. A new mixture algorithm based on scaling of the original distribution is presented and compared to existing algorithms.

    In the second paper, Monte Carlo simulation of quantiles is treated. It is shown that by using importance sampling algorithms developed for tail probability estimation, efficient quantile estimators can be obtained. A functional limit of the quantile process under the importance sampling measure is found, and the variance of the limit process is calculated for regularly varying distributions. The procedure is also applied to the calculation of expected shortfall. The algorithms are illustrated numerically for a heavy-tailed random walk.

    In the third paper, large deviation probabilities for a sum of dependent random variables are derived. The dependence stems from a few underlying random variables, so-called factors. Each summand is composed of two parts: an idiosyncratic part and a part given by the factors. Conditions under which both factors and idiosyncratic components contribute to the large deviation behavior are found, and the resulting approximation is evaluated in a simple example.

    In the fourth paper, the asymptotic eigenvalue distribution of the exponentially weighted moving average covariance estimator is studied. Equations for the asymptotic spectral density and the boundaries of its support are found using the Marchenko-Pastur theorem.

  • 2978.
    Svensson, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Some asymptotic results in dependence modelling2007Licentiate thesis, comprehensive summary (Other scientific)
    Abstract [en]

    This thesis consists of two papers, both devoted to the study of asymptotics in dependence modelling.

    The first paper studies large deviation probabilities for a sum of dependent random variables, where the dependence stems from a few underlying random variables, so-called factors. Each summand is composed of two parts: an idiosyncratic part and a part given by the factors. Conditions under which both factors and idiosyncratic components contribute to the large deviation behaviour are found and the resulting approximation is evaluated in a simple special case. The results are then applied to stochastic processes with the same structure. Based on the results of the first part of the paper, it is concluded that large deviations on a finite time interval are due to one large jump that can come from either the factor or the idiosyncratic part of the process.

    The second paper studies the asymptotic eigenvalue distribution of the exponentially weighted moving average (EWMA) covariance estimator. Equations for the limiting eigenvalue density and the boundaries of its support are found using the Marchenko-Pastur theorem.

  • 2979.
    Svensson, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The asymptotic spectrum of the EWMA covariance estimator2007In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, no 385, p. 621-630Article in journal (Refereed)
    Abstract [en]

    The exponentially weighted moving average (EWMA) covariance estimator is a standard estimator for financial time series, and its spectrum can be used for so-called random matrix filtering. Random matrix filtering using the spectrum of the sample covariance matrix is an established tool in finance and signal detection and the EWMA spectrum can be used analogously. In this paper, the asymptotic spectrum of the EWMA covariance estimator is calculated using the Mar enko-Pastur theorem. Equations for the spectrum and the boundaries of the support of the spectrum are obtained and solved numerically. The spectrum is compared with covariance estimates using simulated i.i.d. data and log-returns from a subset of stocks from the S&P 500. The behaviour of the EWMA estimator in this limited empirical study is similar to the results in previous studies of sample covariance matrices. Correlations in the data are found to only affect a small part of the EWMA spectrum, suggesting that a large part may be filtered out

  • 2980.
    Svensson, Jens
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Large deviations for heavy-tailed factor models2009In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 79, no 3, p. 304-311Article in journal (Refereed)
    Abstract [en]

    We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. Depending on the regions considered, probabilities are determined by different parts of the model.

  • 2981.
    Svärd, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A branch and bound algorithm for evaluation of the Findley fatigue criterion2015In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 73, p. 27-38Article in journal (Refereed)
    Abstract [en]

    In this manuscript, a new algorithm for evaluation of the Findley fatigue criterion is proposed. The algorithm uses a branch and bound technique to limit the number of investigated planes in the search for the critical one. The algorithm has two major advantages over currently existing methods. Firstly, for a given tolerance on the error of the evaluation, it needs to investigate fewer planes on average, thereby reducing the execution time compared to state of the art methods. Secondly, the algorithm is guaranteed to give results within a tolerance of the global maximum, and this tolerance may be freely chosen by the analyst.

  • 2982.
    Svärd, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Interior value extrapolation: a new method for stress evaluation during topology optimization2015In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 51, no 3, p. 613-629Article in journal (Refereed)
    Abstract [en]

    This article presents a new method for evaluating stresses in the jagged structures that arise when using a fixed finite element mesh to optimize the topology of a structure. The new method, Interior Value Extrapolation, IVE, exploits the fact that in the interior of the structure, the stresses calculated by the finite element method are more accurate than at the boundary. The jagged nature of the mesh makes stresses at the boundary oscillate. Therefore, stresses at the boundary are instead extrapolated from results in the interior, resulting in a more stable and accurate stress measure. A restriction method in the form of a non linear density filter is also proposed, tailored to be used in conjunction with the new stress evaluation method. The new method is evaluated for accuracy using example geometries, for which the stresses are known. It is shown that IVE improves the accuracy of the stress calculation. Optimization examples are thereafter solved with and without IVE, and the results are discussed. It is shown that the change in stress evaluation can in fact cause changes in the solution of a typical stress minimization problem.

  • 2983.
    Svärd, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Topology Optimization of Fatigue-Constrained Structures2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Fatigue, or failure of material due to repeated cyclic loading, is one of the most common causes of mechanical failures. The risk of fatigue in a load carrying component is often lowered by adding material, thereby reducing stresses. This increases the component weight, reducing the performance of the component and increasing its manufacturing cost. There is thus a need to design components to be as light as possible, while keeping the risk of fatigue at a low enough level, i.e. there is a need for optimization of the component subject to fatigue constraints

    This thesis deals with design against fatigue using topology optimization, which is a form of structural optimization where an optimal design is sought by using mathematical programming to decide which parts of a design domain should be filled with material, and which should not. 

    To predict fatigue, accurate representation of the geometry and accurate stress computation are of utmost importance. In this thesis, methods for imposing constraints such as minimum inner radii and minimum member sizes in the form of four new density filters are proposed. The filters are able to generate a very sharp representation of the structural boundary. A method for improving the accuracy of stress results at the structural boundary is also proposed, based on extrapolation of results from the interior of the structure. The method gives more accurate stresses, which affects the resulting structures when solving optimization problems. 

    A formulation for fatigue constraints in topology optimization is proposed, based on the weakest link integral. The formulation avoids the problem of choosing between accurate but costly local constraints, and efficient but approximate aggregated constraints, and gives a theoretical motivation for using expressions similar to the p-norm of stresses. 

    For verifying calculations of the fatigue probability of an optimized structure, critical plane criteria are commonly used. A new method for evaluating such criteria using optimization methods is proposed, and is proved to give results within a user given error tolerance. It is shown that compared to existing brute force methods, the proposed method evaluates significantly fewer planes in the search of the critical one.

     

  • 2984.
    Svärd, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Using the weakest link model of fatigue in topology optimizationManuscript (preprint) (Other academic)
    Abstract [en]

    In this work, a method for incorporating fatigue failure in topology op- timization problems is presented. The method is based on the weakest link model of failure, developed by Weibull. The model is based on an assumption on the failure probability of a volume element, as a function of the applied stress. Given some assumptions, the total failure probability of the structure may be calculated as an integral over all elements. In this paper, it is shown that the weakest link model for failure takes a form that is very suitable for topology optimization. In fact, it is shown that the expression for failure probability according to Weibull under some circumstances is very similar to the much used p-norm of stresses. In the paper, the weakest link model is explained in detail, and adaptations to make it suitable for topology optimization are made. Suggestions on how to choose the parameters of the model are given, and the effects of different parameter choices are evaluated using examples. 

  • 2985.
    Swernofsky, Joseph
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Tensor rank is hard to approximate2018In: Leibniz International Proceedings in Informatics, LIPIcs, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2018, article id 26Conference paper (Refereed)
    Abstract [en]

    We prove that approximating the rank of a 3-tensor to within a factor of 1+1/1852-δ, for any δ > 0, is NP-hard over any field. We do this via reduction from bounded occurrence 2-SAT.

  • 2986.
    Szepessy, Anders
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Atomistic and continuum models for phase change dynamics2006In: Proceedings of the International Congress of Mathematicians, 2006, p. 1563-1582Conference paper (Refereed)
    Abstract [en]

    The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and capillary forces acting on length scales compared to the nanometer width of the solid-liquid interface. Its modeling is useful for instance in processing techniques based on casting. The phase field method is widely used to study evolution of such microstructures of phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen�Cahn/Ginzburg�Landau equation modeling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitative correct result of dendritic side branching. This lecture presents some ideas to derive stochastic phase field models from atomistic formulations by coarse-graining molecular dynamics and kinetic Monte Carlo methods.

  • 2987.
    Szepessy, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Langevin molecular dynamics derived from Ehrenfest dynamics2011In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 21, no 11, p. 2289-2334Article in journal (Refereed)
    Abstract [en]

    Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a KacZwanzig setting, with the initial data for the electrons stochastically perturbed from the ground state and the ratio M of nuclei and electron mass tending to infinity. The Ehrenfest nuclei dynamics is approximated by the Langevin dynamics with accuracy o(M-1/2) on bounded time intervals and by o(1) on unbounded time intervals, which makes the small O(M -1/2) friction and o(M-1/2) diffusion terms visible. The initial electron probability distribution is a Gibbs density at low temperature, motivated by a stability and consistency argument. The diffusion and friction coefficients in the Langevin equation satisfy the Einstein's fluctuationdissipation relation.

  • 2988.
    Säterbrink, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hedonic House Price Index2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Nasdaq OMX Valueguard-KTH Housing Index (HOX) is a hedonic price index that illustrates the price development of condominiums in Sweden, and that is obtained by using regression technique. Concerns have been raised regarding the influence of the monthly fee on the index. Low fee condominiums could be more popular because of the low monthly cost, high fee condominiums tend to sell for a lower price due to the high monthly cost. As the price of a condominium rises the importance of the monthly fee decreases. Because of this the monthly fee might affect the regression that produces the index. Furthermore,housing cooperatives are usually indebted. These loans are paid off by the monthly fee which can be considered to finance a debt that few are aware of.

    This issue has been investigated by iteratively estimating the importance of the level of debt in order to find a model that better takes into account the possible impact of the monthly fee on the price development.

    Due to a somewhat simplified model that produces index values with many cases of high standard deviation, no conclusive evidence has been found that confirms the initial hypothesis. Nevertheless, converting part of the monthly fee into debt has shown a general improvement of fitting a regression equation to the data. It is therefore recommended that real data on debt in housing cooperatives be tested in Valuegua

  • 2989.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    An intrinsic definition of the Rees algebra of a moduleIn: Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, E-ISSN 1464-3839Article in journal (Refereed)
    Abstract [en]

    This paper concerns a generalization of the Rees algebra of ideals due to Eisenbud, Huneke and Ulrich that works for any finitely generated module over a noetherian ring. Their definition is in terms of maps to free modules. We give an intrinsic definition using divided powers.

  • 2990.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    AN INTRINSIC DEFINITION OF THE REES ALGEBRA OF A MODULE2018In: Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, E-ISSN 1464-3839, Vol. 61, no 1, p. 13-30Article in journal (Refereed)
    Abstract [en]

    This paper concerns a generalization of the Rees algebra of ideals due to Eisenbud, Huneke and Ulrich that works for any finitely generated module over a noetherian ring. Their definition is in terms of maps to free modules. We give an intrinsic definition using divided powers.

  • 2991.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Good Hilbert functorsManuscript (preprint) (Other academic)
    Abstract [en]

    We introduce the good Hilbert functor and prove that it is algebraic. This functor generalizes various versions of the Hilbert moduli problem, such as the multigraded Hilbert scheme and the invariant Hilbert scheme. Moreover, we generalize a result concerning formal GAGA for good moduli spaces.

  • 2992.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Gotzmann's persistence theorem for finite modules2017In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 477, p. 278-293Article in journal (Refereed)
    Abstract [en]

    We prove a generalization of Gotzmann's persistence theorem in the case of modules with constant Hilbert polynomial. As a consequence, we show that the defining equations that give the embedding of a Quot scheme of points into a Grassmannian are given by a single Fitting ideal.

  • 2993.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Gotzmann's persistence theorem for finite modulesManuscript (preprint) (Other academic)
    Abstract [en]

    We prove a generalization of Gotzmann's persistence theorem in the case of modules with constant Hilbert polynomial. As a consequence, we show that the defining equations that give the embedding of a Quot scheme of points into a Grassmannian are given by a single Fitting ideal.

  • 2994.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Hilbert schemes and Rees algebras2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The topic of this thesis is algebraic geometry, which is the mathematical subject that connects polynomial equations with geometric objects. Modern algebraic geometry has extended this framework by replacing polynomials with elements from a general commutative ring, and studies the geometry of abstract algebra. The thesis consists of six papers relating to some different topics of this field.

    The first three papers concern the Rees algebra. Given an ideal of a commutative ring, the corresponding Rees algebra is the coordinate ring of a blow-up in the subscheme defined by the ideal. We study a generalization of this concept where we replace the ideal with a module. In Paper A we give an intrinsic definition of the Rees algebra of a module in terms of divided powers. In Paper B we show that features of the Rees algebra can be explained by the theory of coherent functors. In Paper C we consider the geometry of the Rees algebra of a module, and characterize it by a universal property.

    The other three papers concern various moduli spaces. In Paper D we prove a partial generalization of Gotzmann’s persistence theorem to modules, and give explicit equations for the embedding of a Quot scheme inside a Grassmannian. In Paper E we expand on a result of Paper D, concerning the structure of certain Fitting ideals, to describe projective embeddings of open affine subschemes of a Hilbert scheme. Finally, in Paper F we introduce the good Hilbert functor parametrizing closed substacks with proper good moduli spaces of an algebraic stack, and we show that this functor is algebraic under certain conditions on the stack. 

  • 2995.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Rees algebras of modules and coherent functorsManuscript (preprint) (Other academic)
    Abstract [en]

    We show that several properties of the theory of Rees algebras of modules become more transparent using the category of coherent functors rather than working directly with modules. In particular, we show that the Rees algebra is induced by a canonical map of coherent functors.

  • 2996.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Rees algebras of modules and Quot schemes of points2014Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of three articles. The first two concern a generalization of Rees algebras of ideals to modules. Paper A shows that the definition of the Rees algebra due to Eisenbud, Huneke and Ulrich has an equivalent, intrinsic, definition in terms of divided powers. In Paper B, we use coherent functors to describe properties of the Rees algebra. In particular, we show that the Rees algebra is induced by a canonical map of coherent functors.

    In Paper C, we prove a generalization of Gotzmann's persistence theorem to finite modules. As a consequence, we show that the embedding of the Quot scheme of points into a Grassmannian is given by a single Fitting ideal.

  • 2997.
    Sædén Ståhl, Gustav
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Total blow-ups of modules and universal flatifications2017In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, no 9, p. 3706-3715Article in journal (Refereed)
    Abstract [en]

    We study the projective spectrum of the Rees algebra of a module, and characterize it by a universal property. As applications, we give descriptions of universal flatifications of modules and of birational projective morphisms.

  • 2998.
    Sædén Ståhl, Gustav
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Skjelnes, Roy
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Explicit projective embeddings of standard opens of the Hilbert scheme of pointsManuscript (preprint) (Other academic)
    Abstract [en]

    We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine of the Grassmannian and a closed stratum determined by a Fitting ideal.

  • 2999.
    Söderberg, Jonas
    KTH, Superseded Departments, Mathematics.
    Artinian level modules and cancellable sequences2004In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 280, no 2, p. 610-623Article in journal (Refereed)
    Abstract [en]

    In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations.

  • 3000.
    Söderberg, Jonas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Artinian level modules of embedding dimension two2006In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 207, no 2, p. 417-432Article in journal (Refereed)
    Abstract [en]

    We prove that a sequence of positive integers (h0, h1,...,h(c)) is the Hilbert function of an artinian level module of embedding dimension two if and only if h(i-1) - 2h(i) + h(i+1) <= 0 for all 0 <= i <= c, where we assume that h(-1) = h(c+1) = 0. This generalizes a result already known for artinian level algebras. We provide two proofs, one using a deformation argument, the other a construction with monomial ideals. We also discuss liftings of artinian modules to modules of dimension one.

57585960616263 2951 - 3000 of 3262
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