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  • 2951. Tausz, Andrew
    et al.
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Adams, Henry
    javaPlex: a research platform for persistent homology2012In: Book of Abstracts: Minisymposium on Publicly Available Geometric/Topological Software, 2012, p. 7-12Conference paper (Refereed)
  • 2952.
    Tavakol, Mehdi
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Tautological Rings of Moduli Spaces of Curves2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The purpose of this thesis is to study tautological rings of moduli spaces of curves. The moduli spaces of curves play an important role in algebraic geometry. The study of algebraic cycles on these spaces was started by Mumford. He introduced the notion of tautological classes on moduli spaces of curves. Faber and Pandharipande have proposed several deep conjectures about the structure of the tautological algebras. According to the Gorenstein conjectures these algebras satisfy a form of Poincaré duality.

    The thesis contains three papers. In paper I we compute the tautological ring of the moduli space of stable n-pointed curves of genus one of compact type. We prove that it is a Gorenstein algebra.

    In paper II we consider the classical case of genus zero and its Chow ring. This ring was originally studied by Keel. He gives an inductive algorithm to compute the Chow ring of the space. Our new construction of the moduli space leads to a simpler presentation of the intersection ring and an explicit form of Keel’s inductive result.

    In paper III we study the tautological ring of the moduli space of stable n-pointed curves of genus two with rational tails. The Gorenstein conjecture is proved in this case as well.

  • 2953.
    Tavakol, Mehdi
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The Chow ring of the moduli space of curves of genus zeroManuscript (preprint) (Other academic)
  • 2954.
    Tavakol, Mehdi
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    THE TAUTOLOGICAL RING OF Mct1,nManuscript (preprint) (Other academic)
  • 2955.
    Tavakol, Mehdi
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The tautological ring of the moduli space Mrt 2,nManuscript (preprint) (Other academic)
  • 2956. Tcheukam, A.
    et al.
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Tembine, H.
    Evacuation of multi-level building: Design, control and strategic flow2016In: Proceedings of the 35th Chinese Control Conference 2016, IEEE Computer Society, 2016, Vol. 2016, p. 9218-9223, article id 7554824Conference paper (Refereed)
    Abstract [en]

    This work introduces a simple mean-field network game that captures some of the key dynamic features of crowd and pedestrian flows in multi-level building evacuations. It considers a route choice by finite number of strategic agents. Each agent state is represented by a simple first order dynamical system. Each agent measures its local congestion measure based on its location in the building. Including the local congestion term and its evolution along the path causes a sort of dispersion of the flow: the agents will try to avoid high density areas in order to reduce their overall walking costs and queuing cost at the exits. Each agent will move to one the closest exits that is safer and that has less congestion through the path. The dynamics of lower layer floors are influenced not only by the agents in that floor but also by the incoming flow from the upper layers through the stairs leading to interacting flows between the floors. Numerics and simulations are carried out to illustrate mean-field equilibria of the evacuation process.

  • 2957.
    Tegerup, Alexander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Simulationof a Bayard-Alpert ionization gauge with the PIC code Warp2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    At RISE Research Institutes of Sweden, there is an interest in computer simulations of the physics related to ionization gauges. The objective of this thesis is to find out if the open source code Warp can be used for simulating the physics of interest.

    In this thesis it is explained what an ionization gauge is and the physics and the governing mathematical equations of the simulations are described. How those governing equations are solved and the algorithms used in Warp is also discussed in this thesis.

    The results of the simulations are presented in the thesis and a discussion of which parts of Warp that need to be further developed to successfully simulate the physics is carried through.  

  • 2958.
    Tegnér, Gustaf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Recurrent neural networks for financial asset forecasting2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The application of neural networks in finance has found renewed interest in the past few years. Neural networks have a proven capability of modeling non-linear relationships and have been proven widely successful in domains such as image and speech recognition. These favorable properties of the Neural Network make them an alluring choice of model when studying the financial markets.

    This thesis is concerned with investigating the use of recurrent neural networks for predicting future financial asset price movements on a set of futures contracts. To aid our research, we compare them to a set of simple feed-forward networks. We conduct further research into the various networks by considering different objective loss functions and how they affect our networks performance. This discussion is extended by considering multi-loss networks as well. The use of different loss functions sheds light on the importance of feature selection. We study a set of simple and complex features and how they affect our model. This aids us in further examining the difference between our networks. Lastly, we analyze of the gradients of our model to provide additional insight into the properties of our features.

    Our results show that recurrent networks provide superior predictive performance compared to feed-forward networks both when evaluating the Sharpe ratio and accuracy. The simple features show better results when optimizing for accuracy. When the network aims to maximize Sharpe, the complex features are preferred. The use of multi-loss networks proved successful when we consider achieving a high Sharpe ratio as our main objective. Our results show significant improved performance compared to a set of simple benchmarks. Through ensemble methods, we achieve a Sharpe ratio of 1.44 and an accuracy of 52.77% on the test set

  • 2959.
    Tempone Olariaga, Raul
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations2002Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. This notion offers a way tounderstand the efficiency of different numerical methods.

    The first paper develops new expansions of the weakcomputational error for Itˆo stochastic differentialequations using Malliavin calculus. These expansions have acomputable leading order term in a posteriori form, and arebased on stochastic flows and discrete dual backward problems.Beside this, these expansions lead to efficient and accuratecomputation of error estimates and give the basis for adaptivealgorithms with either deterministic or stochastic time steps.The second paper proves convergence rates of adaptivealgorithms for Itˆo stochastic differential equations. Twoalgorithms based either on stochastic or deterministic timesteps are studied. The analysis of their numerical complexitycombines the error expansions from the first paper and anextension of the convergence results for adaptive algorithmsapproximating deterministic ordinary differential equations.Both adaptive algorithms are proven to stop with an optimalnumber of time steps up to a problem independent factor definedin the algorithm. The third paper extends the techniques to theframework of Itˆo stochastic differential equations ininfinite dimensional spaces, arising in the Heath Jarrow Mortonterm structure model for financial applications in bondmarkets. Error expansions are derived to identify differenterror contributions arising from time and maturitydiscretization, as well as the classical statistical error dueto finite sampling.

    The last paper studies the approximation of linear ellipticstochastic partial differential equations, describing andanalyzing two numerical methods. The first method generates iidMonte Carlo approximations of the solution by sampling thecoefficients of the equation and using a standard Galerkinfinite elements variational formulation. The second method isbased on a finite dimensional Karhunen- Lo`eve approximation ofthe stochastic coefficients, turning the original stochasticproblem into a high dimensional deterministic parametricelliptic problem. Then, adeterministic Galerkin finite elementmethod, of either h or p version, approximates the stochasticpartial differential equation. The paper concludes by comparingthe numerical complexity of the Monte Carlo method with theparametric finite element method, suggesting intuitiveconditions for an optimal selection of these methods. 2000Mathematics Subject Classification. Primary 65C05, 60H10,60H35, 65C30, 65C20; Secondary 91B28, 91B70.

  • 2960.
    Teneberg, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Pricing Contingent Convertibles using an EquityDerivatives Jump Diusion Approach2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This paper familiarizes the reader with contingent convertibles and their role in the current financial landscape. A contingent convertible is a security behaving like a bond in normal times, but that converts into equity or is written down in times of turbulence. The paper presents a few existing pricing approaches and introduces an extension to one of these, the equity derivatives approach, by letting the underlying asset follow a jump-diffusion process instead of a standard Geometrical Brownian Motion. The extension requires sophisticated computational techniques in order for the pricing to stay within reasonable time frames. Since market data is sparse and incomplete in this area, the validation of the model is not performed quantitatively, but instead supported by qualitative arguments.

  • 2961.
    Tennander, David
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Automatic Projector Calibration for Curved Surfaces Using an Omnidirectional Camera2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This master’s thesis presents one approach to remove distortions generated by projecting onto non flat surfaces. By using an omnidirectional camera a full 360 dome could be calibrated and the corresponding angles between multiple projections could be calculated. The camera was modelled with the Unified Projection Model allowing any omnidirectional camera system to be used. Surface geometry was captured by using Gray code patterns, the optimal image centre was calculated as an quadratic optimisation problem and in the end a Spline surface countering the distortions was generated by using the FAST-LTS regression algorithm. The developed system used a RICOH THETA S camera calibrated by the omnidir module in openCV. A desirable result was achieved and during use of overlapping projectors a maximum error of 0.5° was measured. Testing indicates part of the error could have been introduced in the evaluation measurements. The resulting application is seen as a success and will be used by ÅF Technology AB during calibration of flight simulators.

  • 2962.
    Tewolde Berhan, Damr
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Pricing Inflation Derivatives: A survey of short rate- and market models2012Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis presents an overview of strategies for pricing inflation derivatives. The paper is structured as follows. Firstly, the basic definitions and concepts such as nominal-, real- and inflation rates are introduced. We introduce the benchmark contracts of the inflation derivatives market, and using standard results from no-arbitrage pricing theory, derive pricing formulas for linear contracts on inflation. In addition, the risk profile of inflation contracts is illustrated and we highlight how it’s captured in the models to be studied in the paper.

    We then move on to the main objective of the thesis and present three approaches for pricing inflation derivatives, where we focus in particular on two popular models. The first one, is a so called HJM approach, that models the nominal and real forward curves and relates the two by making an analogy to domestic and foreign fx rates. By the choice of volatility functions in the HJM framework, we produce nominal and real term structures similar to the popular interest-rate derivatives model of Hull-White. This approach was first suggested by Jarrow and Yildirim[1] and it’s main attractiveness lies in that it results in analytic pricing formulas for both linear and non-linear benchmark inflation derivatives.

    The second approach, is a so called market model, independently proposed by Mercurio[2] and Belgrade, Benhamou, and Koehler[4]. Just like the - famous - Libor Market Model, the modeled quantities are observable market entities, namely, the respective forward inflation indices. It is shown how this model as well - by the use of certain approximations - can produce analytic formulas for both linear and non-linear benchmark inflation derivatives.

    The advantages and shortcomings of the respective models are eveluated. In particular, we focus on how well the models calibrate to market data. To this end, model parameters are calibrated to market prices of year-on-year inflation floors; and it is evaluated how well market prices can be recovered by theoretical pricing with the calibrated model parameters. The thesis is concluded with suggestions for possible extensions and improvements.

  • 2963.
    The, Matthew
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Analysis and implementation of anefficient solver for large-scalesimulations of neuronal systems2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Numerical integration methods exploiting the characteristics of neuronal equation systems were investigated. The main observations was a high stiffness and a quasi-linearity of the system. The latter allowed for decomposition into two smaller systems by using a block diagonal Jacobian approximation. The popular backwards differentiation formulas methods (BDF) showed performance degradation for this during first experiments. Linearly implicit peer methods (PeerLI), a new class of methods, did not show this degradation. Parameters for PeerLI were optimized by experimental means and then compared in performance to BDF. Models were simulated in both Matlab and NEURON, a neuron modelling package. For small models PeerLI was competitive with BDF, especially with a block diagonal Jacobian. In NEURON the performance of the block diagonal Jacobian did no longer degrade for BDF, but instead showed degradation for PeerLI, especially for large models. With full Jacobian PeerLI was competitive with BDF, but with block diagonal Jacobian an increase of ca.50% was seen in simulation time. Overall PeerLI methods were competitive for certain problems, but did not give the desired performance gain for block diagonal Jacobian for large problems. There is, however, still a lot of room for improvement, since parameters were only determined experimentally and tuned to small problems.

  • 2964.
    Theorell, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Uncertainty-aware Tracking of Single Bacteria over Image Sequences with Low Frame Rate2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In single-cell analysis, the physiologic states of individual cells are studied. In some studies, the subject of interest is the development over time of some cell characteristic. To obtain time-resolved single-cell data, one possibility is to conduct an experiment on a cell population and make a sequence of images of the population over the course of the experiment. If a mapping is at hand, which determines which cell it is that is the cause of each measured cell in the image sequence, time resolved single-cell data can be extracted. Such a mapping is called a lineage tree, and the process of creating it is called tracking.

    One aim of this work is to develop a tracking algorithm that incorporates organism specific knowledge, such as average division time, in the tracking process. With respect to this aim, a Bayesian model that incorporates biological knowledge is derived, with which every hypothetical lineage tree can be assigned a probability. Additionally, two Monte Carlo algorithms are developed, that approximate the probability distribution of lineage trees given by the Bayesian model. When an approximate distribution is known, for example the most likely lineage tree can be extracted and used.

    In many cases, the information provided to an automatic tracking algorithm is insufficient for the algorithm to find the gold standard lineage tree. In these cases, a possibility is to construct the gold standard lineage tree by manual correction of the lineage tree that has been provided by the tracking algorithm.

    A second aim of this work is to provide a confidence to every assignment in a lineage tree, in order to give the person doing manual corrections useful information about what assignments to change. Such a confidence is provided by the Monte Carlo tracking methods developed in this work.

  • 2965.
    Thi Thanh Truc, Vu
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Testing and optimization of Unicorn Fluid-Structure Interaction solver for simulating an industrial problem2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In industry applications, such as power supply plants, the issue of interaction between fluid and structure is always presented. More precisely, the fluid flow affects the structure by applying force(s) on it and vice versa. As a result, the structure can move (vibrate) or deform. A good understanding of this problem can help to design the system in term of safety, stability and efficiency.

    This project aims to optimize and test the Unicorn FSI solver from the FEniCS project [1] to simulate the interaction of fluid and structure in an experiment, which was carried out at Vattenfall Research and Development. The target is to improve the Unicorn FSI solver to cope with a real industrial problem. Moreover, some results of the simulation can be used as a tool to predict the behavior of a system under the effect of fluid flow

  • 2966.
    Thiele, Lothar
    et al.
    ETH-Zurich, Department of Information Technology and Electrical Engineering.
    Miettinen, Kaisa
    University of Jyväskylä.
    Korhonen, Pekka J.
    Molina, Julián
    University of Malaga, Spain.
    A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization2009In: Evolutionary Computation, ISSN 1063-6560, E-ISSN 1530-9304, Vol. 17, no 3, p. 411-436Article in journal (Refereed)
    Abstract [en]

    In this paper, we discuss the idea of incorporating preference information into evolutionary multi-objective optimization and propose a preference-based evolutionary approach that can be used as an integral part of an interactive algorithm. One algorithm is proposed in the paper. At each iteration, the decision maker is asked to give preference information in terms of his or her reference point consisting of desirable aspiration levels for objective functions. The information is used in an evolutionary algorithm to generate a new population by combining the fitness function and an achievement scalarizing function. In multi-objective optimization, achievement scalarizing functions are widely used to project a given reference point into the Pareto optimal set. In our approach, the next population is thus more concentrated in the area where more preferred alternatives are assumed to lie and the whole Pareto optimal set does not have to be generated with equal accuracy. The approach is demonstrated by numerical examples.

  • 2967.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A recycled characterization of kneading sequences1999In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 9, no 9, p. 1883-1887Article in journal (Refereed)
    Abstract [en]

    For any infinite sequence E on two symbols one can define two sequences of positive integers S(E) (the splitting times) and T(E) (the cosplitting times), which each describe the self-replicative structure of E. If E is the kneading sequence of a unimodal map, it is known that S(E) and T(E) carry a lot of information on the dynamics, and that they are disjoint. We show the reverse implication: A nonperiodic sequence E is the kneading sequence of some unimodal map if the sequences S(E) and T(E) are disjoint.

  • 2968.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Absolutely continuous invariant measures and superstable periodic orbits: weak*-convergence of natural measures1993Report (Other academic)
  • 2969.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Abundance of chaos in one-dimensional population dynamics1999In: International Conference on Differential Equations, Berlin 1999 / [ed] Fiedler B., Gröger K. & Sprekels J., World Scientific, 1999, Vol. 2Conference paper (Refereed)
    Abstract [en]

    We show that strongly chaotic maps appera with poitive frequency in parameter space within both the Ricker family and the Hassel family.

  • 2970.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Feigenbaum Numbers for Certain Flat-Top Families1994In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 3, no 1, p. 51-57Article in journal (Refereed)
  • 2971.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On Approach-Rate Conditions in Unimodal DynamicsManuscript (preprint) (Other academic)
  • 2972.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Periodicity versus chaos in certain population models2000In: Stochastic and Chaotic Dynamics in the Lakes: Stochaos / [ed] D. S. Broomhead, E. A. Luchinskaya, P. V. E. McClintock & T. Mullin, American Institute of Physics (AIP), 2000Conference paper (Refereed)
  • 2973.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Positive exponent in families with flat critical point1999In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 19, no 3, p. 767-807Article in journal (Refereed)
    Abstract [en]

    It is known that in generic, full unimodal families with a critical point of finite order, there exists a set of positive measure in parameter space such that the corresponding maps have chaotic behaviour. In this paper we prove the corresponding statement for certain families of unimodal maps with flat critical point. One of the key-points is a large deviation argument for sums of ‘almost’ independent random variables with only finitely many moments.

  • 2974.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Recurrence of the critical point1993Report (Other academic)
  • 2975.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Some Problems in Unimodal Dynamics1996Doctoral thesis, comprehensive summary (Other academic)
  • 2976.
    Thunberg, Hans
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Tonsättaren Per Nörgårds ''oändlighetsserie"2013In: Normat, ISSN 0801-3500, Vol. 61, no 1, p. 33-47Article in journal (Refereed)
    Abstract [en]

    This article presents a mathematical description, in terms of recursively defined number sequences, of the algorithms devised by the Danish composer Nørgård. The ambition of the latter was to generate from a very short sequence of tones melodies rich in symmetries and selfsimilarities, melodies which could be aperiodic and hence infinite in length. Given the mathematical presentation a variety of results can be formulated and proved. Note that the well-known Thue-Morse sequence is essentially a special case.

  • 2977.
    Thunberg, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Brandell, Gerd
    Lund University.
    Hemmi, Kirsti
    Stockholm University.
    The Widening Gap — A Swedish Perspective2008In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 20, no 2, p. 38-56Article in journal (Refereed)
    Abstract [en]

    Transition problems from secondary to tertiary level in mathematics have been arecurrent issue in Sweden. This paper summarises the development during the lastdecades. Results from two recent research studies that illuminate the transitionproblem are presented. The first one, based on empirical data from a major Swedishtechnical university, characterises the widening gap, in content and in approach,between secondary school and first year university courses. The second study dealswith students’ encounters with mathematical proof and is based on a largeinvestigation at another main Swedish university. We discuss the influence on thecurrent transition problems of school reforms and of the great expansion of highereducation in Sweden during the last 10 – 15 years in view of the results from theresearch studies.

  • 2978.
    Thunberg, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Attitude consensus using networks of uncalibrated cameras2014In: 2014 33rd Chinese Control Conference (CCC), IEEE Computer Society, 2014, p. 1444-1451Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of consensus on SO(3) for networks of uncalibrated cameras. Under the assumption of a pinhole camera model, we prove convergence to the consensus manifold for two types of kinematic control laws, when only conjugate rotation matrices KRK-1 are available among the agents. In these conjugate rotations, the rotation matrices are distorted by the (unknown) intrinsic parameters of the cameras. For the conjugate rotations, we introduce distorted versions of well known local parameterizations of SO(3) and show consensus by using three types of control laws. The control laws are similar to the standard consensus protocol used for systems of agents with single integrator dynamics, where pairwise differences between the states of neighboring agents are used. By considering the restriction to the planar case (when all the rotations have the same rotational axes), we weaken the assumptions on the cameras in the system and consider networks where the camera matrices differ between agents.

  • 2979.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential2018In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 69, no 2, p. 127-130Article in journal (Refereed)
    Abstract [en]

    A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed. Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.

  • 2980.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, P.
    Amplitude-phase calculations of Regge poles obtained from coupled radial Dirac equations2011In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 27, p. 275305-Article in journal (Refereed)
    Abstract [en]

    A recently developed amplitude-phase method for spinor-wave solutions is applied to the calculations of Regge pole positions and residues of Dirac particles. At a given energy the Dirac spin causes two sets of Regge poles that tend to coalesce in the non-relativistic limit. For the particular case of equal Lorentz-type vector and scalar potentials there is only one pole string, located very close to the non-relativistic pole string.

  • 2981.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant2013In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 54, no 5, p. 052301-Article in journal (Refereed)
    Abstract [en]

    It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.

  • 2982.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    McCabe, Patrick
    Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method2017In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 55, no 8, p. 1638-1648Article in journal (Refereed)
    Abstract [en]

    A decomposition of Legendre polynomials into propagating angular waves is derived with the aid of an amplitude-phase method. This decomposition is compared with the 'Nussenzveig/Fuller' so called near/far-side decomposition of Legendre polynomials. The latter decomposition requires the Legendre function of the second kind. This is not the case with the amplitude-phase decomposition. Both representations have the same asymptotic expressions for large values of , where l and are the polynomial degree and the angle respectively. Furthermore, both components of both representations satisfy the Legendre differential equation. However, we show the two representations are not identical.

  • 2983. Tillenius, Martin
    et al.
    Larsson, Elisabeth
    Lehto, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Flyer, Natasha
    A scalable RBF-FD method for atmospheric flow2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 298, p. 406-422Article in journal (Refereed)
    Abstract [en]

    Radial basis function-generated finite difference (RBF-FD) methods have recently been proposed as very interesting for global scale geophysical simulations, and have been shown to outperform established pseudo-spectral and discontinuous Galerkin methods for shallow water test problems. In order to be competitive for very large scale simulations, the RBF-FD methods needs to be efficiently implemented for modern multicore based computer architectures. This is a challenging assignment, because the main computational operations are unstructured sparse matrix-vector multiplications, which in general scale poorly on multicore computers due to bandwidth limitations. However, with the task parallel implementation described here we achieve 60-100% of theoretical speedup within a shared memory node, and 80-100% of linear speedup across nodes. We present results for global shallow water benchmark problems with a 30 km resolution.

  • 2984.
    Tillman, Måns
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    On-Line Market Microstructure Prediction Using Hidden Markov Models2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Over the last decades, financial markets have undergone dramatic changes. With the advent of the arbitrage pricing theory, along with new technology, markets have become more efficient. In particular, the new high-frequency markets, with algorithmic trading operating on micro-second level, make it possible to translate ”information” into price almost instantaneously. Such phenomena are studied in the field of market microstructure theory, which aims to explain and predict them.

    In this thesis, we model the dynamics of high frequency markets using non-linear hidden Markov models (HMMs). Such models feature an intuitive separation between observations and dynamics, and are therefore highly convenient tools in financial settings, where they allow a precise application of domain knowledge. HMMs can be formulated based on only a few parameters, yet their inherently dynamic nature can be used to capture well-known intra-day seasonality effects that many other models fail to explain.

    Due to recent breakthroughs in Monte Carlo methods, HMMs can now be efficiently estimated in real-time. In this thesis, we develop a holistic framework for performing both real-time inference and learning of HMMs, by combining several particle-based methods. Within this framework, we also provide methods for making accurate predictions from the model, as well as methods for assessing the model itself.

    In this framework, a sequential Monte Carlo bootstrap filter is adopted to make on-line inference and predictions. Coupled with a backward smoothing filter, this provides a forward filtering/backward smoothing scheme. This is then used in the sequential Monte Carlo expectation-maximization algorithm for finding the optimal hyper-parameters for the model.

    To design an HMM specifically for capturing information translation, we adopt the observable volume imbalance into a dynamic setting. Volume imbalance has previously been used in market microstructure theory to study, for example, price impact. Through careful selection of key model assumptions, we define a slightly modified observable as a process that we call scaled volume imbalance. The outcomes of this process retain the key features of volume imbalance (that is, its relationship to price impact and information), and allows an efficient evaluation of the framework, while providing a promising platform for future studies. This is demonstrated through a test on actual financial trading data, where we obtain high-performance predictions. Our results demonstrate that the proposed framework can successfully be applied to the field of market microstructure.

  • 2985.
    Timoudas, Thomas Ohlson
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the breakdown of regularity of invariant curves in quasi-periodically forced systems2018Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we study the process of torus collisions in one-parameter families of quasi-periodically forced dynamical systems. Specifically, we study the process whereby two invariant curves (homeomorphic to circles), one attracting and one repelling, bifurcate into a strange non-chaotic attractor. In Paper A, the system is a quasi-periodically forced logistic family, but avoids period-doubling. We give an asymptotic analysis of some geometric properties of the attractor, as it approaches the repeller at the bifurcation point. In Paper B, we study the same type of questions as in Paper A, but instead for a class of quasi-periodic C^2 Schrödinger cocycles. In both papers the results confirm a conjecture that the distance between the curves is asymptotically linear in the parameter, for those classes of systems. In addition, we obtain results about the asymptotic growth of C^1-norms. In Paper C, we study the same class of systems as in Paper B, but instead look at the asymptotics of the (maximal) Lyapunov exponent at the bifurcation point. The results show that it has Hölder exponent exactly 1/2, as the energy parameter approaches the lowest energy of the spectrum. This confirms, for this class and setting, similar conjectures about this asymptotic behaviour.

  • 2986.
    Timoudas, Thomas Ohlson
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Power law asymptotics in the creation of strange attractors in the quasi-periodically forced quadratic family2017In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 30, no 12, p. 4483-4522Article in journal (Refereed)
    Abstract [en]

    Let Phi be a quasi-periodically forced quadratic map, where the rotation constant omega is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under Phi) attracting graph of a nowhere continuous measurable function psi from the circle T to [0, 1]. This paper investigates how a smooth attractor degenerates into a strange one, as a parameter beta approaches a critical value beta(0), and the asymptotics behind the bifurcation of the attractor from smooth to strange. In our model, the cause of the strange attractor is a so-called torus collision, whereby an attractor collides with a repeller. Our results show that the asymptotic minimum distance between the two colliding invariant curves decreases linearly in the parameter beta, as beta approaches the critical parameter value beta(0) from below. Furthermore, we have been able to show that the asymptotic growth of the supremum of the derivative of the attracting graph is asymptotically bounded from both sides by a constant times the reciprocal of the square root of the minimum distance above.

  • 2987.
    Tingstrom, Emil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Modeling and Forecasting Stock Index Returns using Intermarket Factor Models: Predicting Returns and Return Spreads using Multiple Regression and Classication2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The purpose of this thesis is to examine the predictability of stock indices with regression models based on intermarket factors. The underlying idea is that there is some correlation between past price changes and future price changes, and that models attempting to capture this could be improved by including information derived from correlated assets to make predictions of future price changes. The models are tested using the daily returns from Swedish stock indices and evaluated from a portfolio perspective and their statistical signicance. Prediction of the direction of the price is also tested by Support vector machine classication on the OMXS30 index. The results indicate that there is some predictability in the market, in disagreement with the random walk hypothesis.

  • 2988.
    Tingström, Emil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Optimal Investment with Corporate Tax Payments2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This Master's thesis examines the problem of optimal investment when corporate taxes have to be paid on capital gains. Tax payments share a lot of similarities with payoff from a call option where the underlying is the firm's capital. How to optimally deal with this tax-option is a non-trivial problem that is complicated by the feedback between the value of the tax-option and the strategy the firm uses to handle it.

    For the case with only one tax payment it is possible to derive an explicit expression for the optimal strategy using a martingale method. The tax payment introduces some interesting properties to the optimal wealth process, such as a non-zero probability of ending up exactly at the tax basis at the terminal date.  

    The optimal strategy is then generalized to the problem with multiple tax payments using the martingale framework. A numerical method of calculating the optimal strategy based on trinomial trees is also presented and implemented. This is then used to verify the theoretical results and to calculate the optimal strategy with an increasing number of tax payments. 

    For the case with only one tax payment at a terminal date numerical results show that the increase in utility is small and a close to optimal strategy can be derived by ignoring tax. With multiple tax payments however, the increase in utility from using the tax-optimal strategy is significant.

  • 2989.
    Tingström, Victor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Sequential parameter and state learning in continuous time stochastic volatility models using the SMC² algorithm2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this Master’s thesis, joint sequential inference of both parameters and states of stochastic volatility models is carried out using the SMC2 algorithm found in SMC2: an efficient algorithm for sequential analysis of state-space models, Nicolas Chopin, Pierre E. Jacob, Omiros Papaspiliopoulos. The models under study are the continuous time s.v. models (i) Heston, (ii) Bates, and (iii) SVCJ, where inference is based on options prices. It is found that the SMC2 performs well for the simpler models (i) and (ii), wheras filtering in (iii) performs worse. Furthermore, it is found that the FFT option price evaluation is the most computationally demanding step, and it is suggested to explore other avenues of computation, such as GPGPU-based computing.

  • 2990.
    Tkachev, Vladimir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A generalization of Cartan's theorem on isoparametric cubics2010In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 138, no 8, p. 2889-2895Article in journal (Refereed)
    Abstract [en]

    We generalize the well-known result of E. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation vertical bar del f vertical bar(2)= 9 vertical bar x vertical bar(4) must be rotationally equivalent to either x(n)(3) - 3x(n) (x(1)(2) + ... + x(n-1)(2)) or to one of four exceptional Cartan cubic polynomials in dimensions n = 5,8,14,26.

  • 2991.
    Tkachev, Vladimir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Minimal Cubic Cones via Clifford Algebras2010In: Complex Analysis and Operator Theory, ISSN 1661-8254, Vol. 4, no 3, p. 685-700Article in journal (Refereed)
    Abstract [en]

    In this paper, we construct two infinite families of algebraic minimal cones in R-n. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any n >= 4, n not equal 16k + 1, there is at least one minimal cone in R-n given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in R-m2, m >= 2, defined by an irreducible homogeneous polynomial of degree m. These examples provide particular answers to the questions on algebraic minimal cones in R-n posed by Wu-Yi Hsiang in the 1960s.

  • 2992.
    Tkachev, Vladimir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Positive definite collections of disks2006In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 55, no 6, p. 1907-1934Article in journal (Refereed)
    Abstract [en]

    Let Q(z, w) = -IIk=1n [(z - a(k))((w) over bar - (a) over bar (k)) - R-2]. The main rc-sult of the paper states that in the case when the nodes a(j) are situated at the vertices of a regular n-gon inscribed in the unit circle, the matrix Q (a(i), a(j)) is positive definite if and only if R < rho(n), where z = 2 rho(2)(n) - 1 is the smallest not equal -1 zero of the Jacobi polynomial P-v(n-2v,-1) (z), v = [n/2].

  • 2993.
    Tkachev, Vladimir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Ullemar's formula for the moment map, II2005In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 404, no 1-3, p. 380-388Article in journal (Refereed)
    Abstract [en]

    We prove the complex analogue of Ullemar's formula for the Jacobian of the complex moment mapping. This formula was previously established in the real case.

  • 2994.
    Tkachev, Vladimir G.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Disjoint minimal graphs2009In: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 35, no 2, p. 139-155Article in journal (Refereed)
    Abstract [en]

    We prove that the number s(n) of disjoint minimal graphs supported on domains in R-n is bounded by e(n + 1)(2). In the two-dimensional case, we show that s(2) <= 3.

  • 2995.
    Torell, Björn
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Name Concentration Risk and Pillar 2 Compliance: The Granularity Adjustment2013Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    A credit portfolio where each obligor contributes infinitesimally to the risk is said to be infinitely granular. The risk related to the fact that no real credit portfolio is infinitely granular, is called name concentration risk.

    Under Basel II, banks are required to hold a capital buffer for credit risk in order to sustain the probability of default on an acceptable level. Credit risk capital charges computed under pillar 1 of Basel II have been calibrated for a specific level of name concentration. If a bank deviates from this benchmark it is expected to address this under pillar 2, which may involve increased capital charges.

    Here, we look at some of the difficulties that a bank may encounter when computing a name concentration risk add-on under pillar 2. In particular, we study the granularity adjustment for the Vasicek and CreditRisk+ models. An advantage of this approach is that no vendor software products are necessary. We also address the questions of when the granularity adjustment is a coherent risk measure and how to allocate the add-on to exposures in order to optimize the credit portfolio. Finally, the discussed models are applied to real data

  • 2996.
    Tornberg, Anna-Karin
    NYU.
    Numerical Simulations of the Dynamics of Fiber Suspensions2005In: Multiscale Methods in Science and Engineering, Springer, 2005, p. 275-289Chapter in book (Refereed)
    Abstract [en]

    The dynamics of flexible fibers or filaments immersed in a fluid are important to understanding many interesting problems arising in biology, engineering, and physics. For most applications, the flows are at very low Reynolds numbers, and the fibers can have aspect ratios of length to radius from a few tens to several thousands. This class of problems is difficult to solve accurately to a reasonable cost with grid based methods, partly due to the different scales in length and radius of the fibers and the fact that elastic equations must be solved within the fibers. Making explicit use both of the fact that we are considering Stokes flow, as well as of the slenderness of the fibers, we have designed a cost-effective method to simulate multiple interacting elastic fibers in a three dimensional Stokes flow. The key points are that for Stokes flow, boundary integral methods can be employed to reduce the three-dimensional dynamics to the dynamics of the two-dimensional fiber surfaces, and that using slender body asymptotics, this can be further reduced to the dynamics of the one-dimensional fiber center-lines. The resulting integral equations include both the effect of the fibers on the flow field, as well as the interactions of fibers, as mediated by the flow. We have developed a numerical method based on this theory that allows for simulating multiple interacting highly flexible fibers. Considering the efficiency of the method, another important fact is that the framework is suitable for introducing a semi-implicit time-stepping scheme, eliminating the severe constraint on the time-step size arising from the elasticity. Our numerical approach is based on second-order divided differences for spatial derivatives, combined with special product integration methods that reflect the nearly singular nature of the integral operators

  • 2997.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Regularization techniques for singular source terms in differential equations2005In: European Congress of Mathematics: Stockholm, June 27-July 2, 2004 / [ed] Ari Laptev, Zurich: European Mathematical Society Publishing House, 2005, p. 477-499Chapter in book (Refereed)
  • 2998.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    The Ewald sums for singly, doubly and triply periodic electrostatic systems2015In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 42, p. 227-248Article in journal (Refereed)
    Abstract [en]

    When evaluating the electrostatic potential, periodic boundary conditions in one, two or three of the spatial dimensions are often required for different applications. The triply periodic Ewald summation formula is classical, and Ewald summation formulas for the other two cases have also been derived. In this paper, derivations of the Ewald sums in the doubly and singly periodic cases are presented in a uniform framework based on Fourier analysis, which also yields a natural starting point for FFT-based fast summation methods.

  • 2999.
    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

  • 3000.
    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.

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