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  • 251.
    Ariel, Gil
    et al.
    Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
    Engquist, Björn
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Tsai, Richard
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    A multiscale method for stiff ordinary differential equations with resonance2009Ingår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 78, nr 266, s. 929-956Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A multiscale method for computing the effective behavior of a class of stiff and highly oscillatory ordinary differential equations (ODEs) is presented. The oscillations may be in resonance with one another and thereby generate hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables whose dynamics is closed up to perturbation, and is sufficient to approximate any variable and functional that are slow under the dynamics of the ODE. This set of variables is detected numerically as a preprocessing step in the numerical methods. Error and complexity estimates are obtained. The advantages of the method is demonstrated with a few examples, including a commonly studied problem of Fermi, Pasta, and Ulam.

  • 252.
    Ariel, Gil
    et al.
    Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
    Engquist, Björn
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Tsai, Richard
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    A reversible multiscale integration method2009Ingår i: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 7, nr 3, s. 595-610Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A multiscale, time reversible method for computing the effective slow behavior of systems of highly oscillatory ordinary differential equations is presented. The proposed method relies on correctly tracking a set of slow variables that is sufficient to approximate any variable and functional that are slow under the dynamics of the system. The algorithm follows the framework of the heterogeneous multiscale method. The notion of time reversibility in the multiple time-scale setting is discussed. The algorithm requires nontrivial matching between the microscopic state variables and the macroscopic slow ones. Numerical examples show the efficiency of the multiscale method and the advantages of time reversibility.

  • 253.
    Ariel, Gil
    et al.
    Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
    Engquist, Björn
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Tsai, Richard
    Department of Mathematics, The University of Texas at Austin, Austin, USA.
    Numerical multiscale methods for coupled oscillators2009Ingår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 7, nr 3, s. 1387-1404Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A multiscale method for computing the effective slow behavior of a system of weakly coupled nonlinear planar oscillators is presented. The oscillators may be either in the form of a periodic solution or a stable limit cycle. Furthermore, the oscillators may be in resonance with one another and thereby generate some hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables that is sufficient to approximate any variable and functional that are slow under the dynamics of the ordinary differential equation. The technique is more efficient than existing methods, and its advantages are demonstrated with examples. The algorithm follows the framework of the heterogeneous multiscale method.

  • 254.
    Arjmand, Doghonay
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Analysis and Applications of Heterogeneous Multiscale Methods for Multiscale Partial Differential Equations2015Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis centers on the development and analysis of numerical multiscale methods for multiscale problems arising in steady heat conduction, heat transfer and wave propagation in heterogeneous media. In a multiscale problem several scales interact with each other to form a system which has variations over a wide range of scales. A direct numerical simulation of such problems requires resolving the small scales over a computational domain, typically much larger than the microscopic scales. This demands a tremendous computational cost. We develop and analyse multiscale methods based on the heterogeneous multiscale methods (HMM) framework, which captures the macroscopic variations in the solution at a cost much lower than traditional numerical recipes. HMM assumes that there is a macro and a micro model which describes the problem. The micro model is accurate but computationally expensive to solve. The macro model is inexpensive but incomplete as it lacks certain parameter values. These are upscaled by solving the micro model locally in small parts of the domain. The accuracy of the method is then linked to how accurately this upscaling procedure captures the right macroscopic effects. In this thesis we analyse the upscaling error of existing multiscale methods and also propose a micro model which significantly reduces the upscaling error invarious settings. In papers I and IV we give an analysis of a finite difference HMM (FD-HMM) for approximating the effective solutions of multiscale wave equations over long time scales. In particular, we consider time scales T^ε = O(ε−k ), k =1, 2, where ε represents the size of the microstructures in the medium. In this setting, waves exhibit non-trivial behaviour which do not appear over short time scales. We use new analytical tools to prove that the FD-HMM accurately captures the long time effects. We first, in Paper I, consider T^ε =O(ε−2 ) and analyze the accuracy of FD-HMM in a one-dimensional periodicsetting. The core analytical ideas are quasi-polynomial solutions of periodic problems and local time averages of solutions of periodic wave equations.The analysis naturally reveals the role of consistency in HMM for high order approximation of effective quantities over long time scales. Next, in paperIV, we consider T^ε = O(ε−1 ) and use the tools in a multi-dimensional settingto analyze the accuracy of the FD-HMM in locally-periodic media where fast and slow variations are allowed at the same time. Moreover, in papers II and III we propose new multiscale methods which substantially improve the upscaling error in multiscale elliptic, parabolic and hyperbolic partial differential equations. In paper II we first propose a FD-HMM for solving elliptic homogenization problems. The strategy is to use the wave equation as the micro model even if the macro problem is of elliptic type. Next in paper III, we use this idea in a finite element HMM setting and generalize the approach to parabolic and hyperbolic problems. In a spatially fully discrete a priori error analysis we prove that the upscaling error can be made arbitrarily small for periodic media, even if we do not know the exact period of the oscillations in the media.

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    Thesis
  • 255.
    Arjmand, Doghonay
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Analysis and Applications of the Heterogeneous Multiscale Methods for Multiscale Elliptic and Hyperbolic Partial Differential Equations2013Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis concerns the applications and analysis of the Heterogeneous Multiscale methods (HMM) for Multiscale Elliptic and Hyperbolic Partial Differential Equations. We have gathered the main contributions in two papers.

    The first paper deals with the cell-boundary error which is present in multi-scale algorithms for elliptic homogenization problems. Typical multi-scale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. Solving the micro model requires, on the other hand, imposing boundary conditions on the boundary of the microscopic domain. Imposing a naive boundary condition leads to $O(\varepsilon/\eta)$ error in the computation, where $\varepsilon$ is the size of the microscopic variations in the media and $\eta$ is the size of the micro-domain. Until now, strategies were proposed to improve the convergence rate up to fourth-order in $\varepsilon/\eta$ at best. However, the removal of this error in multi-scale algorithms still remains an important open problem. In this paper, we present an approach with a time-dependent model which is general in terms of dimension. With this approach we are able to obtain $O((\varepsilon/\eta)^q)$ and $O((\varepsilon/\eta)^q  + \eta^p)$ convergence rates in periodic and locally-periodic media respectively, where $p,q$ can be chosen arbitrarily large.     

    In the second paper, we analyze a multi-scale method developed under the Heterogeneous Multi-Scale Methods (HMM) framework for numerical approximation of wave propagation problems in periodic media. In particular, we are interested in the long time $O(\varepsilon^{-2})$ wave propagation. In the method, the microscopic model uses the macro solutions as initial data. In short-time wave propagation problems a linear interpolant of the macro variables can be used as the initial data for the micro-model. However, in long-time multi-scale wave problems the linear data does not suffice and one has to use a third-degree interpolant of the coarse data to capture the $O(1)$ dispersive effects apperaing in the long time. In this paper, we prove that through using an initial data consistent with the current macro state, HMM captures this dispersive effects up to any desired order of accuracy in terms of $\varepsilon/\eta$. We use two new ideas, namely quasi-polynomial solutions of periodic problems and local time averages of solutions of periodic hyperbolic PDEs. As a byproduct, these ideas naturally reveal the role of consistency for high accuracy approximation of homogenized quantities.

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    Thesis_Intro
  • 256.
    Arjmand, Doghonay
    et al.
    Dep. of Math., Fatih University, Istanbul, Turkey.
    Ashyralyev, Allaberen
    Dep. of Elect. and Electr. Eng., Bogazici University, Istanbul, Turkey.
    A note on the Taylor s decomposition on four points for a third-order differential equation2007Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, ISSN 0096-3003, Vol. 188, nr 2, s. 1483-1490Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Taylor's decomposition on four points is presented. three-step difference schemes generated by the Taylor's decomposition on fourpoints for the numerical solutions of an initial-value problem, a boundary-value problem, and a nonlocal boundary-value problem for a third-order ordinary differential equation are constructed. Numerical examples are given.

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    article1
  • 257. Arjmand, Doghonay
    et al.
    Runborg, Olof
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    A time dependent approach for removing the cell boundary error in elliptic homogenization problems2016Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 314, s. 206-227Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper concerns the cell-boundary error present in multiscale algorithms for elliptic homogenization problems. Typical multiscale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. To solve the micro model, boundary conditions are required on the boundary of the microscopic domain. Imposing a naive boundary condition leads to O(epsilon/eta) error in the computation, where epsilon is the size of the microscopic variations in the media and eta is the size of the micro-domain. The removal of this error in modern multiscale algorithms still remains an important open problem. In this paper, we present a time-dependent approach which is general in terms of dimension. We provide a theorem which shows that we have arbitrarily high order convergence rates in terms of epsilon/eta in the periodic setting. Additionally, we present numerical evidence showing that the method improves the O(epsilon/eta) error to O(epsilon) in general non-periodic media.

  • 258.
    Arjmand, Doghonay
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA. KTH, Centra, SeRC - Swedish e-Science Research Centre.
    Runborg, Olof
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA. KTH, Centra, SeRC - Swedish e-Science Research Centre.
    Analysis of heterogeneous multiscale methods for long time wave propagation problems2014Ingår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 12, nr 3, s. 1135-1166Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we analyze a multiscale method developed under the heterogeneous multiscale method (HMM) framework for numerical approximation of multiscale wave propagation problems in periodic media. In particular, we are interested in the long time O(epsilon(-2)) wave propagation, where e represents the size of the microscopic variations in the media. In large time scales, the solutions of multiscale wave equations exhibit O(1) dispersive effects which are not observed in short time scales. A typical HMM has two main components: a macromodel and a micromodel. The macromodel is incomplete and lacks a set of local data. In the setting of multiscale PDEs, one has to solve for the full oscillatory problem over local microscopic domains of size eta = O(epsilon) to upscale the parameter values which are missing in the macroscopic model. In this paper, we prove that if the microproblems are consistent with the macroscopic solutions, the HMM approximates the unknown parameter values in the macromodel up to any desired order of accuracy in terms of epsilon/eta..

  • 259.
    Arjmand, Doghonay
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Runborg, Olof
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Analysis of HMM for Long Time Multiscale Wave Propagation Problems in Locally-Periodic MediaManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Multiscale wave propagation problems are difficult to solve numerically due to the interaction of different scales inherent in the problem. Extracting information about the average behaviour of the system requires resolving small scales in the problem. This leads to a tremendous computational burden if the size of microscopic variations are much smaller than the size of scales of interest. Heterogeneous multiscale methods (HMM) is a tool to avoid resolving the small scales everywhere. Nevertheless, it approximates the average part of the solution by upscaling the microscopic information on a small part of the domain. This leads to a substantial improvement in the computational cost. In this article, we analyze an HMM-based numerical method which approximates the long time behaviour of multiscale wave equations. In particular, we consider theoretically challenging case of locally-periodic media where fast and slow variations are allowed at the same time. We are interested in the long time regime (T=O(e^{-1})), where e represents the wavelength of the fast variations in themedia. We first use asymptotic expansions to derive effective equations describing the long time effects of the multiscale waves in multi-dimensional locally-periodic media. We then show that HMM captures these non-trivial long time eects. All the theoretical statements are general in terms of dimension. Two dimensional numericale xamples are considered to support our theoretical arguments

  • 260. Arjmand, Doghonay
    et al.
    Runborg, Olof
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA. KTH, Centra, SeRC - Swedish e-Science Research Centre.
    Estimates for the upscaling error in heterogeneous multiscale methods for wave propagation problems in locally periodic media2017Ingår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 15, nr 2, s. 948-976Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the microscopic variations over a much larger physical domain of interest. The heterogeneous multiscale method (HMM) is an efficient framework to approximate the solutions of multiscale problems. In the HMM, one assumes an incomplete macroscopic model which is coupled to a known but expensive microscopic model. The micromodel is solved only locally to upscale the parameter values which are missing in the macro model. The resulting macroscopic model can then be solved at a cost independent of the small scales in the problem. In general, the accuracy of the HMM is related to how good the upscaling step approximates the right macroscopic quantities. The analysis of the method that we consider here was previously addressed only in purely periodic media, although the method itself is numerically shown to be applicable to more general settings. In the present study, we consider a more realistic setting by assuming a locally periodic medium where slow and fast variations are allowed at the same time. We then prove that the HMM captures the right macroscopic effects. The generality of the tools and ideas in the analysis allows us to establish convergence rates in a multidimensional setting. The theoretical findings here imply an improved convergence rate in one dimension, which also justifies the numerical observations from our earlier study.

  • 261.
    Arjmand, Doghonay
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.). KTH, Centra, SeRC - Swedish e-Science Research Centre.
    Stohrer, Christian
    A FINITE ELEMENT HETEROGENEOUS MULTISCALE METHOD WITH IMPROVED CONTROL OVER THE MODELING ERROR2016Ingår i: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 14, nr 2, s. 463-487Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Multiscale partial differential equations (PDEs) are difficult to solve by traditional numerical methods due to the need to resolve the small wavelengths in the media over the entire computational domain. We develop and analyze a Finite Element Heterogeneous Multiscale Method (FE-HMM) for approximating the homogenized solutions of multiscale PDEs of elliptic, parabolic, and hyperbolic type. Typical multiscale methods require a coupling between a micro and a macro model. Inspired from the homogenization theory, traditional FE-HMM schemes use elliptic PDEs as the micro model. We use, however, the second order wave equation as our micro model independent of the type of the problem on the macro level. This allows us to control the modeling error originating from the coupling between the different scales. In a spatially fully discrete a priori error analysis we prove that the modeling error can be made arbitrarily small for periodic media, even if we do not know the exact period of the oscillations in the media. We provide numerical examples in one and two dimensions confirming the theoretical results. Further examples show that the method captures the effective solutions in general non-periodic settings as well.

  • 262.
    Arjmand, Doghonay
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Stohrer, Christian
    ENSTA ParisTech.
    A Finite Element Heterogenous Multiscale Method with Improved Control Over the Modeling ErrorManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Multiscale partial dierential equations (PDEs) are difficult to solve by traditional numerical methods due to the need to resolve the small wavelengths in the media over the entire computational domain. We develop and analyze a Finite Element Heterogeneous Multiscale Method (FE-HMM) for approximating the homogenized solutions of multiscale PDEs of elliptic, parabolic,and hyperbolic type. Typical multiscale methods require a coupling between a micro and a macromodel. Inspired from the homogenization theory, traditional FE-HMM schemes use elliptic PDEs as the micro model. We use, however, the second order wave equation as our micro model independent of the type of the problem on the macro level. This allows us to control the modeling error originating by the coupling between the dierent scales. In a spatially fully discrete a priori error analysis we prove that the modeling error can be made arbitrarily small for periodic media, even if we do not know the exact period of the oscillations in the media. We provide numerical examples in one and two dimensions confirming the theoretical results. Further examples show that the method captures the effective solutions in general non-periodic settings as well

  • 263.
    Armerin, Fredrik
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande, Bygg- och fastighetsekonomi.
    American perpetual options with random start2019Ingår i: Results in Applied Mathematics, ISSN 2590-0374, Vol. 3, artikel-id 100017Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the valuation of American perpetual options with the property that they are only possible to exercise after the occurrence of a random time, which is a stopping time with respect to a given filtration. One situation where this feature is present is when making an irreversible investment, e.g. building on vacant land, while waiting for a permit to be allowed to do so. The random time in this case is the time at which the permit is given. This and the value of a version of an abandonment option are given as two applications of this modelling framework. 

  • 264.
    Armerin, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    An axiomatic approach to the valuation of cash flows2014Ingår i: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, Vol. 2014, nr 1, s. 32-40Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.

  • 265.
    Armerin, Fredrik
    KTH, Tidigare Institutioner, Matematik.
    Aspects of cash-flow valuation2004Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    This thesis consists of five papers. In the first two papers we consider a general approach to cash flow valuation, focusing on dynamic properties of the value of a stream of cash flows. The third paper discusses immunization theory, where old results are shown to hold in general deterministic models, but often fail to be true in stochastic models. In the fourth paper we comment on the connection between arbitrage opportunities and an immunized position. Finally, in the last paper we study coherent and convex measure of risk applied to portfolio optimization and insurance.

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    FULLTEXT01
  • 266.
    Armerin, Fredrik
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Centra, Centrum för bank och finans, Cefin.
    On some properties of elliptical distributions2017Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We look at a characterization of elliptical distributions in the case when finiteness of moments of the random vector is not assumed. Some additional results regarding elliptical distributions are also presented.

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    fulltext
  • 267.
    Armerin, Fredrik
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Centra, Centrum för bank och finans, Cefin.
    The Conditional Quantile as a Minimizer2014Rapport (Övrigt vetenskapligt)
    Abstract [en]

    It is well known that a quantile is the solution to a minimization problem.We show that the conditional quantile with respect to a general -algebrais the solution to similar a minimization problem.

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    fulltext
  • 268.
    Armerin, Fredrik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Astrup Jensen, Bjarne
    Copenhagen Business School.
    Björk, Tomas
    Stockholm School of Economics.
    Term Structure Models with Parallel and Proportional Shifts2007Ingår i: Applied Mathematical Finance, ISSN 1350-486X, E-ISSN 1433-4313, Vol. 14, nr 3, s. 243-260Artikel i tidskrift (Refereegranskat)
    Abstract [en]

        We investigate the possibility of an arbitrage free model for the term structure of in-terest rates where the yield curve only changes through a parallel shift. We consider HJMtype forward rate models driven by a multidimensional Wiener process as well as by a gen-eral marked point process. Within this general framework we show that there does indeedexist a large variety of nontrivial parallel shift term structure models, and we also describethese in detail. We also show that there exists no nontrivial flat term structure model. Thesame analysis is repeated for the similar case, where the yield curve only changes throughproportional shifts.

  • 269.
    Armerin, Fredrik
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande, Bygg- och fastighetsekonomi.
    Hallgren, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Koski, Timo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Forecasting Ranking in Harness Racing Using Probabilities Induced by Expected Positions2019Ingår i: Applied Artificial Intelligence, ISSN 0883-9514, E-ISSN 1087-6545, Vol. 33, nr 2, s. 171-189Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Ranked events are pivotal in many important AI-applications such as Question Answering and recommendations systems. This paper studies ranked events in the setting of harness racing. For each horse there exists a probability distribution over its possible rankings. In the paper, it is shown that a set of expected positions (and more generally, higher moments) for the horses induces this probability distribution. The main contribution of the paper is a method, which extracts this induced probability distribution from a set of expected positions. An algorithm is proposed where the extraction of the induced distribution is given by the estimated expectations. MATLAB code is provided for the methodology. This approach gives freedom to model the horses in many different ways without the restrictions imposed by for instance logistic regression. To illustrate this point, we employ a neural network and ordinary ridge regression. The method is applied to predicting the distribution of the finishing positions for horses in harness racing. It outperforms both multinomial logistic regression and the market odds. The ease of use combined with fine results from the suggested approach constitutes a relevant addition to the increasingly important field of ranked events.

  • 270.
    Armerin, Fredrik
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande.
    Han-Suck, Song
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Fastigheter och byggande.
    Valuation of real options in incomplete models – An implied yield approach2018Ingår i: Fuzzy Economic Review, ISSN 1136-0593, Vol. 23, nr 1, s. 19-32Artikel, forskningsöversikt (Refereegranskat)
    Abstract [en]

    In many applications of real options there is an assumption of complete capital markets. For the perpetual timing option this means that if the underlying asset does not pay out any cash flows, then there is no finite optimal time at which the investment should be undertaken. In contrast, when the market is incomplete there is a possibility of having a finite optimal stopping time even in the cases when the underlying asset does not pay out any cash flows. We discuss the incomplete case in models driven by both Brownian motion(s) and a Poisson process and connect it with the concept of an implied yield. The implied yield will in these models extend the concept of a monetary yield (i.e. a yield that represents the fraction of the value of an asset paid out as a cash flow). Several examples of incomplete market models where there could be a finite optimal time to invest are given.

  • 271.
    Arnarson, Teitur
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Early exercise boundary regularity close to expiry in the indifference setting: A PDE approachArtikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    The free boundary problem that occurs when pricing American options is studied in a general setting. We investigate the regularity of the free boundary close to initial state using the so called blow-up technique. This problem has been studied extensively and good results are known for the linear, one-dimensional case. The blow-up technique, however, works also for non-linear PDE in higher dimensions. For illustration we apply the technique to the indierence pricing model where the involved PDE is non-linear.

  • 272.
    Arnarson, Teitur
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    PDE methods for free boundary problems in financial mathematics2008Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it. In Papers I–II we obtain boundary regularity results by local analysis of the PDEs involved and in Paper III we perform local analysis of the corresponding stochastic representation.

    The last paper is different in its character as we are dealing with an optimal switching problem, where a switching of state occurs when the underlying process crosses a free boundary. Here we obtain existence and regularity results of the viscosity solutions to the involved system of variational inequalities.

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  • 273.
    Arnarson, Teitur
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    The blow-up technique in terms of stochastics applied to optimal stopping problems in financeManuskript (Övrigt vetenskapligt)
    Abstract [en]

    The blow-up technique is a useful tool for local analysis in PDEtheory. It is applicable to non-linear, higher dimensional PDEs. In this paperwe translate the blow-up technique to stochastic terms by considering thestochastic representation of solutions to PDEs. For illustration we apply theblow-up technique to obtain the early exercise boundary regularity close to expiryfor American put and call options in the classic Black-Scholes framework.

  • 274.
    Arnarson, Teitur
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Poghosyan, Michael
    Yerevan State Univ, Dept Math & Mech.
    Shahgholian, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    A PDE approach to regularity of solutions to finite horizon optimal switching problems2009Ingår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, nr 12, s. 6054-6067Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C-l,C-l-regular away for the free boundaries of the action sets.

  • 275.
    Arnarson, Teitur
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Eriksson, Jonatan
    On the size of the non-coincidence set of parabolic obstacle problems with applications to American option pricing2007Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 101, nr 1, s. 148-160Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The following paper is devoted to the study of the positivity set U = {L phi > 0} arising in parabolic obstacle problems. It is shown that U is contained in the non-coincidence set with a positive distance between the boundaries uniformly in the spatial variable if the boundary of U satisfies an interior C-1 -Dini condition in the space variable and a Lipschitz condition in the time variable. We apply our results to American option pricing and we thus show that the positivity set is strictly contained in the continuation region, which means that the option should not be exercised in U or on the boundary of U.

  • 276.
    Arnlind, Joakim
    KTH, Tidigare Institutioner, Matematik.
    Eigenvalue dynamics and membrane solutions2004Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
  • 277.
    Arnlind, Joakim
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Graph Techniques for Matrix Equations and Eigenvalue Dynamics2008Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    One way to construct noncommutative analogues of a Riemannian manifold Σ is to make use of the Toeplitz quantization procedure. In Paper III and IV, we construct C-algebras for a continuously deformable class of spheres and tori, and by introducing the directed graph of a representation, we can completely characterize the representation theory of these algebras in terms of the corresponding graphs. It turns out that the irreducible representations are indexed by the periodic orbits and N-strings of an iterated map s:(reals) 2→(reals)2 associated to the algebra. As our construction allows for transitions between spheres and tori (passing through a singular surface), one easily sees how the structure of the matrices changes as the topology changes.

    In Paper II, noncommutative analogues of minimal surface and membrane equations are constructed and new solutions are presented -- some of which correspond to minimal tori embedded in S7.

    Paper I is concerned with the problem of finding differential equations for the eigenvalues of a symmetric N × N matrix satisfying Xdd=0.

    Namely, by finding N(N-1)/2 suitable conserved quantities, the time-evolution of X (with arbitrary initial conditions), is reduced to non-linear equations involving only the eigenvalues of Χ.

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  • 278.
    Arnlind, Joakim
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Representation theory of C-algebras for a higher order class of spheres and tori2008Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, nr 5, s. 053502-1-053502-13Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of "loop" and "string" representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the "Henon algebras," for which the dynamical map is a generalized Henon map, and give an example where irreducible representations of all dimensions exist.

  • 279. Arnlind, Joakim
    et al.
    Choe, Jaigyoung
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Noncommutative Minimal Surfaces2016Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, nr 8, s. 1109-1129Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We define noncommutative minimal surfaces in the Weyl algebra, and give a method to construct them by generalizing the well-known Weierstrass representation.

  • 280.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Discrete minimal surface algebras2010Ingår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 6, s. Paper 042,18-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl(n) (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d <= 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is ( generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  • 281.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Eigenvalue dynamics, Follytons and large N limits of matrices2006Ingår i: Applications of Random Matrices in Physics / [ed] Brezin, E; Kazakov, V; Serban, D; Wiegmann, P; Zabrodin, A, DORDRECHT: SPRINGER , 2006, Vol. 221, s. 89-94Konferensbidrag (Refereegranskat)
    Abstract [en]

    How do the eigenvalues of a “free” hermitian N × N matrix X(t) evolve in time? The answer is provided by the rational Calogero-Moser systems [5, 13] if (!) the initial conditions are chosen such that i[X(0),Ẋ(0)] has a non-zero eigenvalue of multiplicity N–1; for generic X(0),Ẋ(0) the question remained unanswered for 30 years.

  • 282.
    Arnlind, Joakim
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Hoppe, Jens
    KTH, Tidigare Institutioner, Matematik.
    Eigenvalue Dynamics off the Calogero-Moser system2004Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, nr 2, s. 121-129Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.

  • 283.
    Arnlind, Joakim
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Huisken, Gerhard
    Max Planck Institute for Gravitational Physics.
    Multi linear formulation of differential geometry and matrix regularizations2012Ingår i: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 91, nr 1, s. 1-39Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that many aspects of the differential geometry of em-bedded Riemannian manifolds can be formulated in terms of multilinear algebraic structures on the space of smooth functions. Inparticular, we find algebraic expressions for Weingarten’s formula,the Ricci curvature and the Codazzi-Mainardi equations.For matrix analogues of embedded surfaces we define discretecurvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressionsfor the discrete Gauss curvature in terms of matrices representingthe embedding coordinates, and explicit examples are provided.Furthermore, we illustrate the fact that techniques from differen-tial geometry can carry over to matrix analogues by proving thata bound on the discrete Gauss curvature implies a bound on theeigenvalues of the discrete Laplace operator.

  • 284.
    Arnlind, Joakim
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Hoppe, Jens
    KTH, Tidigare Institutioner, Matematik.
    Theisen, Stefan
    Albert Einstein Inst.
    Spinning Membranes2004Ingår i: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 599, nr 1-2, s. 118-128Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdS(p) X S-q, as well as in flat space-time. Nontrivial reductions of the BMN matrix model equations are also given.

  • 285.
    Arnoldsson, Jakob
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    OptimalSpeed Controller for a Heavy-Duty Vehicle in the Presence of SurroundingTraffic2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Denna avhandling har undersökt intelligenta och bränsleeffektiva hastighetsregulator för tunga fordon, givet ett framförvarande fordon.  En modell prediktiv kontroller (MPC), hastighetsregulator, har utvecklats tillsammans med en PI-regulator som referens. Den MPC-baserade regulatorn använder information om framtida trafikförhållanden, så som vägtopografi, hastighetsbegränsningar och hastighet hos framförvarande fordon för att ta bränsleeffektiva beslut.  Simuleringar har gjorts för ett så kallat Deterministiskt fall, vilket betyder att MPC regulatorn får fullständig information om framtida trafikförhållanden, och ett Stokastiskt fall där den framtida hastigheten hos framförvarande fordon måste predikteras. För det första fallet ingår regenerativ bromsning samt en enkel distansberoende modell för luftmotståndskoefficienten. För det andra fallet skapas tre prediktionsmodeller: två regelbaserade modeller (konstant hastighet, konstant acceleration) och en inlärningsmodell, Nonlinear Auto Regressive eXogenouse model (NARX).

    Datorsimuleringar har gjorts, både på skapade testfall och på loggade data från ett Scania fordon. De utvecklade modellerna utvärderas slutligen på testfallen för både varierande massor och tillåtna avvikelser från det framförvarande fordonet. Simuleringarna visar på potential för bränslebesparingar med MPC-baserade hastighetsregulatorer både för det deterministiska och det stokastiska fallet.

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  • 286. Aro, Helena
    et al.
    Djehiche, Boualem
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Löfdahl, Björn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Stochastic modelling of disability insurance in a multi-period framework2015Ingår i: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, nr 1, s. 88-106Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data.

  • 287.
    Aronsson, Petter
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ronneback Thomson, Joachim
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Optimal löptidsallokering av bostadslån2014Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Föreliggande kandidatarbete introducerar en dynamisk allokeringsmetod för bostadslån som kan användas till att reducera ett växande samhällsproblem. De svenska hushållens skulder ökar allt mer och det är belåning till följd finansiering av fastighet som är den främsta orsaken. På grund av en lång tids stigande bostadspriser är svenskarna mer belånade än någonsin [1]. Med tilltagande räntenivå ökar risken att inte klara av räntekostnaderna som huvudsakligen är den största ekonomiska kostnaden för de flesta hushåll.

    Så långt har diskussion emellertid saknats beträffande betydelsen av effektiva och säkra bostadslån. Med hjälp av den dynamiska allokeringsmetoden optimeras löptidsfördelningen av bostadslån, historiskt och prognostiserat. I det senare fallet minimeras både förväntad räntekostnad och risk. Mer specifikt tar metoden hänsyn till tre risknivåer som lägger olika vikt på förväntad räntekostnad gentemot risk. Syftet med arbetet att kunna tillämpa metoden i verkligheten som ett beslutstöd samt kommersialisera som en affärsidé.

    Modelleringen av bostadslån som ett nätverk är centralt för den dynamiska allokeringsmetoden. Detta tillvägagångssätt gör det möjligt att studera ett bostadslån under en längre period vilket är nödvändigt för att kunna hitta en optimal löptidsallokering. Resultatet för det historiska fallet visar att det oftast varit fördelaktigt med rörlig löptid på bostadslånet. Dock inte i lika stor utsträckning som förmodats - enbart under sju av de senaste sjutton åren. Dessutom indikerar resultaten för det prognostiserade fallet att det är fördelaktigt att binda bostadslån på längre löptider. Avslutningsvis presenteras en affärsmodell för det nystartade bolaget Looptime AB vars affärsidé är att förvalta fastighetslån för privatpersoner, bostadsrättsföreningar och icke-finansiella företag.

  • 288.
    Arridge, Simon
    et al.
    UCL, Dept Comp Sci, Gower St, London WC1E 6BT, England..
    Maass, Peter
    Univ Bremen, Dept Math, Postfach 330 440, D-28344 Bremen, Germany..
    Öktem, Ozan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Schonlieb, Carola-Bibiane
    Univ Cambridge, Dept Appl Math & Theoret Phys, Wilberforce Rd, Cambridge CB3 0WA, England..
    Solving inverse problems using data-driven models2019Ingår i: Acta Numerica, ISSN 0962-4929, E-ISSN 1474-0508, Vol. 28, s. 1-174Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical-analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

  • 289. Arruda, Lynnyngs Kelly
    et al.
    Lenells, Jonatan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Long-time asymptotics for the derivative nonlinear Schrodinger equation on the half-line2017Ingår i: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 30, nr 11, s. 4141-4172Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive asymptotic formulas for the solution of the derivative nonlinear Schrodinger equation on the half-line under the assumption that the initial and boundary values lie in the Schwartz class. The formulas clearly show the effect of the boundary on the solution. The approach is based on a nonlinear steepest descent analysis of an associated Riemann-Hilbert problem.

  • 290. Arsenlis, Athanasios
    et al.
    Cai, Wei
    Tang, Meijie
    Rhee, Moono
    Oppelstrup, Tomas
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Hommes, Gregg
    Pierce, Tom G.
    Bulatov, Vasily V.
    Enabling strain hardening simulations with dislocation dynamics2007Ingår i: Modelling and Simulation in Materials Science and Engineering, ISSN 0965-0393, E-ISSN 1361-651X, Vol. 15, s. 553-595Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Numerical algorithms for discrete dislocation dynamics simulations areinvestigated for the purpose of enabling strain hardening simulations of singlecrystals on massively parallel computers. The algorithms investigated includethe O(N) calculation of forces, the equations of motion, time integration,adaptive mesh refinement, the treatment of dislocation core reactions and thedynamic distribution of data and work on parallel computers. A simulationintegrating all these algorithmic elements using the Parallel DislocationSimulator (ParaDiS) code is performed to understand their behaviour in concertand to evaluate the overall numerical performance of dislocation dynamicssimulations and their ability to accumulate percent of plastic strain.

  • 291.
    Ashant, Aidin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Hakim, Elisabeth
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Quantitative Portfolio Construction Using Stochastic Programming2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.

    Ladda ner fulltext (pdf)
    fulltext
  • 292.
    Ashfaq, Awais
    et al.
    KTH. Halmstad University, Sweden.
    Adler, Jonas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta Instrument AB, Sweden.
    A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images2017Ingår i: IFMBE Proceedings, Springer, 2017, s. 531-538Konferensbidrag (Refereegranskat)
    Abstract [en]

    CBCT images suffer from acute shading artifacts primarily due to scatter. Numerous image-domain correction algorithms have been proposed in the literature that use patient-specific planning CT images to estimate shading contributions in CBCT images. However, in the context of radiosurgery applications such as gamma knife, planning images are often acquired through MRI which impedes the use of polynomial fitting approaches for shading correction. We present a new shading correction approach that is independent of planning CT images. Our algorithm is based on the assumption that true CBCT images follow a uniform volumetric intensity distribution per material, and scatter perturbs this uniform texture by contributing cupping and shading artifacts in the image domain. The framework is a combination of fuzzy C-means coupled with a neighborhood regularization term and Otsu’s method. Experimental results on artificially simulated craniofacial CBCT images are provided to demonstrate the effectiveness of our algorithm. Spatial non-uniformity is reduced from 16% to 7% in soft tissue and from 44% to 8% in bone regions. With shading- correction, thresholding based segmentation accuracy for bone pixels is improved from 85% to 91% when compared to thresholding without shading-correction. The proposed algorithm is thus practical and qualifies as a p lug and p lay extension into any CBCT reconstruction software for shading correction.

  • 293. Ashyralyev, Allaberen
    et al.
    Arjmand, Doghonay
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Koksal, Muhammet
    Taylor's decomposition on four points for solving third-order linear time-varying systems2009Ingår i: Journal of the Franklin Institute, ISSN 0016-0032, E-ISSN 1879-2693, Vol. 346, nr 7, s. 651-662Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the present paper, the use of three-step difference schemes generated by Taylor's decomposition on four points for the numerical solutions of third-order time-varying linear dynamical systems is presented. The method is illustrated for the numerical analysis of an up-converter used in communication systems.

  • 294.
    Asinowski, A.
    et al.
    Alpen Adria Univ Klagenfurt, Klagenfurt, Austria..
    Banderier, C.
    Univ Paris 13, Villetaneuse, France..
    Billey, S.
    Univ Washington, Seattle, WA 98195 USA..
    Hackl, B.
    Alpen Adria Univ Klagenfurt, Klagenfurt, Austria..
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    POP-STACK SORTING AND ITS IMAGE: PERMUTATIONS WITH OVERLAPPING RUNS2019Ingår i: Acta Mathematica Universitatis Comenianae, ISSN 0862-9544, E-ISSN 0231-6986, Vol. 88, nr 3, s. 395-402Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Pop-stack sorting is an important variation for sorting permutations via a stack. A single iteration of pop-stack sorting is the transformation T : S-n -> S-n that reverses all the maximal descending sequences of letters in a permutation. We investigate structural and enumerative aspects of pop-stacked permutations - the permutations that belong to the image of S-n under T. This work is part of a project aiming to provide the full combinatorial analysis of sorting with a pop-stack, as it was successfully done for sorting with a stack (though, even in this case, some famous problems are still open). The first results already show that pop-stack sorting has a very rich combinatorial structure, and leads to surprising phenomena.

  • 295. Asmussen, Sören
    et al.
    Rydén, Tobias
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A Note on Skewness in Regenerative Simulation2011Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 40, nr 1, s. 45-57Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The purpose of this article is to show, empirically and theoretically, that performance evaluation by means of regenerative simulation often involves random variables with distributions that are heavy tailed and heavily skewed. This, in turn, leads to the variance of estimators being poorly estimated, and confidence intervals having actual coverage quite different from (typically lower than) the nominal one. We illustrate these general ideas by estimating the mean occupancy and tail probabilities in M/G/1 queues, comparing confidence intervals computed from batch means to various intervals computed from regenerative cycles. In addition, we provide theoretical results on skewness to support the empirical findings.

  • 296.
    Aspenberg, Magnus
    KTH, Tidigare Institutioner, Matematik.
    The Collet-Eckmann condition for rational functions on the Riemann sphere2004Doktorsavhandling, monografi (Övrigt vetenskapligt)
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  • 297.
    Aspenberg, Magnus
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Yampolsky, Michael
    Mating Non-Renormalizable Quadratic Polynomials2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 287, nr 1, s. 1-40Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.

  • 298.
    Atai, Farrokh
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Hallnäs, Martin
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models2014Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, nr 7, s. 811-835Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the relativistic generalization of the quantum A (N-1) Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh-Feigin-Veselov-Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.

  • 299.
    Atai, Farrokh
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hynek, Mariusz
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Variational orthogonalizationManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.

  • 300.
    Athanasiou, George
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Weeraddana, Pradeep Chathuranga
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Fischione, Carlo
    KTH, Skolan för elektro- och systemteknik (EES), Reglerteknik.
    Association control in millimeterWave wireless access networks2014Ingår i: 2014 IEEE 19th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks, CAMAD 2014, 2014, s. 260-264Konferensbidrag (Refereegranskat)
    Abstract [en]

    The resource allocation problem of optimal assignment of the stations to the available access points in 60 GHz millimeterWave wireless access networks is investigated. The problem is posed as a multi-assignment optimization problem. The proposed solution method converts the initial problem to a minimum cost flow problem and allows to design an efficient algorithm by a combination of auction algorithms. The solution algorithm exploits the network optimization structure of the problem, and thus is much more powerful than computationally intensive general-purpose solvers. Theoretical and numerical results evince numerous properties, such as optimality, convergence, and scalability in comparison to existing approaches.

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