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  • 201.
    Andersson, Lars
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Backdahl, Thomas
    Blue, Pieter
    A NEW TENSORIAL CONSERVATION LAW FOR MAXWELL FIELDS ON THE KERR BACKGROUND2017Ingår i: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 105, nr 2, s. 163-176Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this construction works for the Kerr spacetime.

  • 202.
    Andersson, Lars
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.). Max Planck Institute for Gravitational Physics, United Kingdom.
    Blue, P.
    Hidden symmetries and decay for the wave equation on the Kerr spacetime2015Ingår i: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 182, nr 3, s. 787-853Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalisation of the vector-field method that allows the use of higher-order symmetry operators. In particular, our method makes use of the second-order Carter operator, which is a hidden symmetry in the sense that it does not correspond to a Killing symmetry of the spacetime.

  • 203.
    Andersson, Lars
    et al.
    KTH, Tidigare Institutioner, Matematik.
    Dahl, Mattias
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Howard, Ralph
    Boundary and lens rigidity of Lorentzian surfaces1996Ingår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 348, s. 2307-2329Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let g be a Lorentzian metric on the plane ℝ2 that agrees with the standard metric g0 = -dx2 + dy2 outside a compact set and so that there are no conjugate points along any time-like geodesic of (ℝ2, g). Then (ℝ2, g) and (ℝ2, g0) are isometric. Further, if (M*, g*) and (M*, p*) are two dimensional compact time oriented Lorentzian manifolds with space-like boundaries and so that all time-like geodesies of (M, g) maximize the distances between their points and (M, g) and (M*, g*) are "boundary isometric", then there is a conformal diffeomorphism between (M, g) and (M*, g*) and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

  • 204.
    Andersson, Lars Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.). Albert Einstein Institute, Germany.
    Bäckdahl, T.
    Blue, P.
    Decay of solutions to the Maxwell equation on the Schwarzschild background2016Ingår i: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, nr 8, artikel-id 085010Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor Hab defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current Hab (∂t)b. The tensor Hab vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.

  • 205.
    Andersson, Markus
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Multivariate Financial Time Series and Volatility Models with Applications to Tactical Asset Allocation2015Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Den finansiella marknaden är av en väldigt komplex struktur och modelleringsteknikerna har under senare tid blivit allt mer komplicerade. För en portföljförvaltare är det av yttersta vikt att finna mer sofistikerade modelleringstekniker, speciellt efter finanskrisen 2007-2008. Idéen i den här uppsatsen är att finna ett samband mellan makroekonomiska faktorer och aktieportföljer innehållande tillgångar från OMX Stockholm 30 och använda dessa för att utföra Tactial Asset Allocation (TAA). Mer specifikt är målsättningen att visa att dynamiska modelleringstekniker har ett bättre utfall än mer statiska modeller i portföljteori.

  • 206.
    Andersson, Markus
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Singh, Nirankar
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    EN UNDERSÖKNING KRING PRISPÅVERKAN VID INRÄTTANDE AV EN NYBYGGNATION.2013Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Den här rapporten är riktad till byggbolag och mäklare som är intresserade

    av att se hur prisutvecklingen på äldre bebyggelse är kring ett nybyggnadsprojekt.

    Det kan tänkas att det är lättare för byggbolag att få igenom bygglov

    om det kan påvisas att nybyggnadsprojekt har en positiv inverkan på priset

    gällande närliggande byggnation. Studien får dock ses som ett pilotprojekt

    då arbeten av den här typen är ovanliga och troligen inte utförda tidigare i

    Sverige. Modellen behöver utvidgas med fler områden för att kunna säkerställa

    resultatet med högre signifikans.

    Slutsatsen kring studien är att det finns indikation på positiv prispåverkan,

    men modelleringen och tillvägagångssättet har varit det centrala i studien.

    Det är troligt att anta att för att göra en så god modell som möjligt behövs

    även fler faktorer beaktas. Exempelvis kan det tänkas att då ett nybyggnadsprojekt

    byggs, förbättras även kommunikationerna till området det kan

    byggas nya butiker eller motsvarande förbättringar, så även sådana aspekter

    skulle behövas för en mer rigorös studie.

  • 207.
    Andersson, Martin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Constructing Multidimensional Dynamical Systems with Positive Lyapunov Exponents2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    I denna uppsats anpassar vi Marcelo Vianas generella konstruktion av  glatta transformationer som uppvisar icke-likformig expansion i flera  dimensioner. I vår konstruktion, istället för att koppla ihop vårt system med en kvadratisk avbildning, får vi expansionen från en avbildning med en  kubisk kritisk punkt. Dessutom så diskuterar vi hur argumentationen kan  utvidgas och expansionen fås av vissa typer av avbildningar med en kritisk punkt av godtyckligt hög (udda) grad. Vi diskuterar också problemen i att försöka använda Vianas metod med den så kallade "double standard"-avbildningen som källan till den icke-likformiga expansionen.

  • 208.
    Andersson, Nicole
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Söderberg, Petra
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    A study of the most important volume drivers for sparkling wine in Sweden2015Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    I denna uppsats undersöks de faktorer som påverkar den sålda volymen av mousserande vin. Regressionsanalys används för att modellera sambandet mellan de identifierade parametrarna och volymen.

    Den sociala hållbarheten i och med en avreglering av Sveriges alkoholmarknad kommer att undersökas med hjälp av en 5C-analys av Systembolaget, WACOSS’s Social Sustainability framework samt Social Life’s framework.

    Parametrarna som påverkade den sålda volymen mest föll under tre olika kategorier: Land, vilken typ av vindruva vinet är gjort på samt pris per liter. De flesta parametrarna visade sig ha en positiv påverkan på den sålda volymen, med undantag för viner från Nya Zeeland samt högre pris.

    Denna uppsats kommer fram till slutsatsen att en reglerad alkoholmarknad är gynnsam när syftet är att hålla alkoholkonsumtionen låg och den övergripande folkhälsan hög.

  • 209. Andersson, O.
    et al.
    Argenton, C.
    Weibull, Jörgen W.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.). Stockholm School of Economics, Sweden.
    Robustness to strategic uncertainty in the Nash demand game2018Ingår i: Mathematical Social Sciences, ISSN 0165-4896, E-ISSN 1879-3118, Vol. 91, s. 1-5Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper studies the role of strategic uncertainty in the Nash demand game. A player's uncertainty about another player's strategy is modeled as an atomless probability distribution over that player's strategy set. A strategy profile is robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others (Andersson et al., 2014). In the context of the Nash demand game, we show that robustness to symmetric (asymmetric) strategic uncertainty singles out the (generalized) Nash bargaining solution. The least uncertain party obtains the bigger share.

  • 210. Andersson, Ola
    et al.
    Argenton, Cedric
    Weibull, Jörgen W.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Robustness to strategic uncertainty2014Ingår i: Games and Economic Behavior, ISSN 0899-8256, E-ISSN 1090-2473, Vol. 85, nr 1, s. 272-288Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a criterion for robustness to strategic uncertainty in games with continuum strategy sets. We model a player's uncertainty about another player's strategy as an atomless probability distribution over that player's strategy set. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others. When payoff functions are continuous we show that our criterion is a refinement of Nash equilibrium and we also give sufficient conditions for existence of a robust strategy profile. In addition, we apply the criterion to Bertrand games with convex costs, a class of games with discontinuous payoff functions and a continuum of Nash equilibria. We show that it then selects a unique Nash equilibrium, in agreement with some recent experimental findings.

  • 211.
    André, Léo
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Prediction of French day-ahead electricity prices: Comparison between a deterministic and a stochastic approach2015Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Denna avhandling behandlar den nya flödesbaserade beräkningsmetoden som används i Centrala Västeuropa på ekonomisidan. Målet är att producera tillförlitliga metoder för prognostisering. Två tillvägagångssätt kan användas: den första är baserad på en deterministisk och algoritmisk metod som inbegriper studier av interaktionen mellan fundamenta och priserna. Den andra är en mer statistisk metod som bygger på en tidsseriemodellering av de franska flödesbaserade priserna. Båda tillvägagångssätten har fördelar och nackdelar som kommer som diskuteras i det följande. Arbetet är främst

    baserade på globala simulerade data från CASC i genomförandefasen av

    flödesbasen i Västeuropa.

  • 212.
    Andréasson, Håkan
    et al.
    Chalmers.
    Ringström, Hans
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Proof of the cosmic no-hair conjecture in the T3-Gowdy symmetric Einstein-Vlasov setting2016Ingår i: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 18, nr 7, s. 1565-1650Artikel i tidskrift (Refereegranskat)
  • 213.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Adaptive node distribution for on-line trajectory planning2006Ingår i: ICAS-Secretariat - 25th Congress of the International Council of the Aeronautical Sciences 2006, Curran Associates, Inc., 2006, s. 3150-3157Konferensbidrag (Refereegranskat)
    Abstract [en]

    Direct methods for trajectory optimization are traditionally based on a priori temporal dis- cretization and collocation methods. In this work, the problem of node distribution is for- mulated as an optimization problem, which is to be included in the underlying non-linear mathematical programming problem (NLP). The benefits of utilizing the suggested method for on-line trajectory optimization are illustrated by a missile guidance example.

  • 214.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Adaptive Node Distribution for Online Trajectory PlanningManuskript (Övrigt vetenskapligt)
  • 215.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    On Cooperative Surveillance, Online Trajectory Planning and Observer Based Control2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for  online  trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a  unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.

  • 216.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Online trajectory planning and observer based control2006Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.

    The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.

    Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.

    In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.

    Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.

  • 217.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hamberg, Johan
    Riemannian Observers for Euler-Lagrange Systems2005Ingår i: Proceedings of the 16th IFAC World Congress: Prague, Czech Republic, July 3-8, 2005, 2005, s. 115-120Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analysed. This observer is an generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contractivity is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. The convergence properties of the observer are illustrated by an example where the configuration manifold is the three-dimensional sphere, S3.

  • 218.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Active Observers for Mobile Robotic SystemsManuskript (Övrigt vetenskapligt)
    Abstract [en]

    An important class of non-uniformly observable systems come from applications in mobile robotics. In this paper, the problem of active observer design for such systems is considered. The set of feasible configurations and the set of output flow equivalent states is defined. It is shown that the inter-relation between these two sets serves as the basis for design of active observers. The proposed observer design method is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.

  • 219.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Lindskog, Therese
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Ögren, Petter
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Algorithms for the connectivity constrained unmanned ground vehicle surveillance problem2009Ingår i: European Control Conference (ECC), Budapest, Hungary: EUCA , 2009Konferensbidrag (Refereegranskat)
    Abstract [en]

    The Connectivity Constrained UGV Surveillance Problem (CUSP) considered in this paper is the following. Given a set of surveillance UGVs and a user defined area to be covered, find waypoint-paths such that; 1) the area is completely surveyed, 2) the time for performing the search is minimized and 3) the induced information graph is kept recurrently connected. It has previously been shown that the CUSP is NP-hard. This paper presents four different heuristic algorithms for solving the CUSP, namely, the Token Station Algorithm, the Stacking Algorithm, the Visibility Graph Algorithm and the Connectivity Primitive Algorithm. These algorithms are then compared by means of Monte Carlo simulations. The conclusions drawn are that the Token Station Algorithm provides the most optimal solutions, the Stacking Algorithm has the lowest computational complexity, while the Connectivity Primitive Algorithm provides the best trade-off between optimality and computational complexity for larger problem instances.

  • 220.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ögren, Petter
    Minimum time multi-UGV surveillance2008Ingår i: OPTIMIZATION AND COOPERATIVE CONTROL STRATEGIES / [ed] Hirsch MJ; Commander CW; Pardalos PM; Murphey R, Berlin: Springer Verlag , 2008, s. 31-45Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper addresses the problem of concurrent task- and path planning for a number of  surveillance Unmanned Ground Vehicles (UGVs) such that a user defined area of interest is covered by the UGVs' sensors in minimum time. We first formulate the problem, and show that it is in fact  a generalization of the Multiple Traveling Salesmen Problem (MTSP), which is known to be NP-hard. We then propose a solution that decomposes the problem into three subproblems. The first is to find a maximal convex covering of the search area. Most results on static coverage  use disjoint partitions of the search area, e.g. triangulation, to convert the continuous sensor positioning problem into a  discrete one. However, by a simple example, we show that a highly overlapping set of maximal convex sets is better suited for  minimum time coverage. The second subproblem is a combinatorial assignment and ordering of the sets in the cover.  Since Tabu search algorithms are known to perform well on various routing problems,  we use it as a part of our proposed solution. Finally, the third subproblem utilizes a particular shortest path sub-routine in order to find the vehicle paths, and calculate the overall objective function used in the Tabu search. The proposed algorithm is illustrated by a number of simulation examples.

  • 221.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Ögren, Petter
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Communication constrained multi-UGV surveillance2008Ingår i: IFAC World Congress, Seoul, Korea, 2008Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper addresses the problem of connectivity constrained surveillance of a given polyhedral area with obstacles using a group of Unmanned Ground Vehicles (UGVs). The considered communication restrictions may involve both line-of-sight constraints and limited sensor range constraints. In this paper, the focus is on dynamic information graphs, G, which are required to be kept recurrently connected. The main motivation for introducing this weaker notion of connectivity is security and surveillance applications where the sentry vehicles may have to split temporary in order to complete the given mission efficiently but are required to establish contact recurrently in order to exchange information or to make sure that all units are intact and well-functioning. From a theoretical standpoint, recurrent connectivity is shown to be sufficient for exponential convergence of consensus filters for the collected sensor data.

  • 222. Anisi, David A.
    et al.
    Ögren, Petter
    Swedish Defence Research Agency (FOI), Sweden.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Cooperative Minimum Time Surveillance With Multiple Ground Vehicles2010Ingår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, nr 12, s. 2679-2691Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we formulate and solve two different minimum time problems related to unmanned ground vehicle (UGV) surveillance. The first problem is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensors' field of view are assumed to have a limited coverage range and be occluded by the obstacles. The second problem extends the first by additionally requiring the induced information graph to be connected at the time instants when the UGVs perform the surveillance mission, i.e., when they gather and transmit sensor data. In the context of the second problem, we also introduce and utilize the notion of recurrent connectivity, which is a significantly more flexible connectivity constraint than, e.g., the 1-hop connectivity constraints and use it to discuss consensus filter convergence for the group of UGVs.

  • 223. Anisi, David A.
    et al.
    Ögren, Petter
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Lindskog, Therese
    Cooperative Surveillance Missions with Multiple Unmanned Ground Vehicles (UGVs)2008Ingår i: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, s. 2444-2449Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper proposes an optimization based approach to multi-UGV surveillance. In particular, we formulate both the minimum time- and connectivity constrained surveillance problems, show NP-hardness of them and propose decomposition techniques that allow us to solve them efficiently in an algorithmic manner. The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensor's field of view are assumed to be occluded by the obstacles and limited by a maximal sensor range. The connectivity constrained formulation extends the first by additionally requiring that the information graph induced by the sensors is connected at the time instants when the UGVs stop to perform the surveillance task. The second formulation is relevant to situation when mutual visibility is needed either to transmit the sensor data being gathered, or to protect the team from hostile persons trying to approach the stationary UGVs.

  • 224.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ögren, Petter
    Department of Autonomous Systems Swedish Defence Research Agency.
    Robinson, John W. C.
    Department of Autonomous Systems Swedish Defence Research Agency.
    Safe receding horizon control of an aerial vehicle2006Ingår i: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, IEEE , 2006, s. 57-62Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper addresses the problem of designing a real time high performance controller and trajectory generator for air vehicles. The control objective is to use information about terrain and enemy threats to fly low and avoid radar exposure on the way to a given target. The proposed algorithm builds on the well known approach of Receding Horizon Control (RHC) combined with a terminal cost, calculated from a graph representation of the environment. Using a novel safety maneuver, and under an assumption on the maximal terrain inclination, we are able to prove safety as well as task completion. The safety maneuver is incorporated in the short term optimization, which is performed using Nonlinear Programming (NLP). Some key characteristics of the trajectory planner are highlighted through simulations.

  • 225.
    Anisi, David
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Robinson, John W.C.
    Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Ögren, Petter
    Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Online Trajectory Planning for Aerial Vehicle: A Safe Approach with Guaranteed Task CompletionManuskript (Övrigt vetenskapligt)
    Abstract [en]

    On-line trajectory optimization in three dimensional space is the main topic of the paper at hand. The high-level framework augments on-line receding horizon control with an off-line computed terminal cost that captures the global characteristics of the environment, as well as any possible mission objectives. The first part of the paper is devoted to the single vehicle case while the second part considers the problem of simultaneous arrival of multiple aerial vehicles. The main contribution of the first part is two-fold. Firstly, by augmenting a so called safety maneuver at the end of the planned trajectory, this paper extends previous results by addressing provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method presented is shown to have finite time task completion. Moreover, a quantitative comparison between the two competing objectives of optimality and computational tractability is made. Finally, some other key characteristics of the trajectory planner, such as ability to minimize threat exposure and robustness, are highlighted through simulations. As for the simultaneous arrival problem considered in the second part, by using a time-scale separation principle, we are able to adopt standard Laplacian control to a consensus problem which is neither unconstrained, nor first order. 

  • 226.
    Anisi, David
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Robinson, John W.C.
    Swedish Defence Research Agency (FOI), Department of Aeronautics .
    Ögren, Petter
    Swedish Defence Research Agency (FOI).
    On-line Trajectory planning for aerial vehicles: a safe approach with guaranteed task completion2006Ingår i: Collection of Technical Papers: AIAA Guidance, Navigation, and Control Conference 2006, 2006, s. 914-938Konferensbidrag (Refereegranskat)
    Abstract [en]

    On-line trajectory optimization in three dimensional space is the main topic of the paper at hand. The high-level framework augments on-line receding horizon control with an off-line computed terminal cost that captures the global characteristics of the environment, as well as any possible mission objectives. The first part of the paper is devoted to the single vehicle case while the second part considers the problem of simultaneous arrival of multiple aerial vehicles. The main contribution of the first part is two-fold. Firstly, by augmenting a so called safety maneuver at the end of the planned trajectory, this paper extends previous results by addressing provable safety properties in a 3 D setting. Secondly, assuming initial feasibility, the planning method presented is shown to have finite time task completion. Moreover, a quantitative comparison between the two competing objectives of optimality and computational tractability is made. Finally, some other key characteristics of the trajectory planner, such as ability to minimize threat exposure and robustness, are highlighted through simulations. As for the simultaneous arrival problem considered in the second part, by using a time-scale separation principle, we are able to adopt standard Laplacian control to a consensus problem which is neither unconstrained, nor first order.

  • 227.
    Annink, Marit
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Larsson, Rebecca
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Introduction of the Academic Factor Quality Minus Junk to a Commercial Factor Model and its Effect on the Explanatory Power. An OLS Regression on Stock Returns2019Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Förmågan att förutsäga aktiers avkastning önskar många besitta, och på ett så precist sätt som möjligt. Under många år har forskning pågått inom området för faktormodeller som förklarar avkastningar, med målet att öka modellernas förklaringsgrad. Detta är dock en komplex verksamhet eftersom faktorerna och deras förbättring av förklaringsgraden måste vara signifikanta för modellen. Då och då kommer forskare fram med nya sådana faktorer som har positiv påverkan på modeller. AQR Capital Management är inget undantag eftersom de 2013 presenterade sin faktor Quality Minus Junk som visar signifikanta riskjusterade avkastningar. Detta kandidatexamensarbete inom matematisk statistik och industriell ekonomi, ämnar att utreda huruvida den kommersiella faktormodellen som används på Fjärde AP-fonden förbättras genom tillägget av faktorn Quality Minus Junk, i förklaringsgradsmening. Metoden som används är till största delen baserad på multipel linjär regression och tre treårsperioder studeras i tidsintervallet 2010 till 2018. Resultaten från detta projekt visar på att faktorn Quality Minus Junk bidrar med signifikanta ökningar av förklaringsgraden för en av tre perioder, den senaste perioden 2016-2018. Eftersom resultaten är inkonklusiva krävs vidare studier för att bättre förstå och konkludera vad dessa resultat faktiskt innebär samt för att inkludera QMJ-faktorn i modellen eller ej.

  • 228. Arakelyan, A.
    et al.
    Shah Gholian, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Multi-Phase Quadrature Domains and a Related Minimization Problem2016Ingår i: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, s. 1-21Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.

  • 229. Arakelyan, A.
    et al.
    Shahgholian, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Prajapat, J. V.
    Two-and multi-phase quadrature surfaces2017Ingår i: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 16, nr 6, s. 2023-2045Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we shall initiate the study of the two-and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of view that (for two-phase case) relates to integral representation where dsx is the surface measure, μ = μ+-μ-is given measure with support in (a priori unknown domain) ω = ω+ [ω-, g is a given smooth positive function, and the integral holds for all functions h, which are harmonic on ω. Our approach is based on minimization of the corresponding two-and multiphase functional and the use of its one-phase version as a barrier. We prove several results concerning existence, qualitative behavior, and regularity theory for solutions. A central result in our study states that three or more junction points do not appear.

  • 230.
    Arakelyan, Avetik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    The Finite Difference Method for Two-Phase Parabolic Obstacle-Like Problem: Like ProblemArtikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    In this paper for two-phase parabolic obstacle-like problem, \[\Delta u -u_t=\lambda^+\cdot\chi_{\{u>0\}}-\lambda^-\cdot\chi_{\{u<0\}},\quad (t,x)\in (0,T)\times\Omega,\] where $T < \infty, \lambda^+ ,\lambda^- > 0$ are Lipschitz continuous functions, and $\Omega\subset\mathbb{R}^n$ is a bounded domain, we will introduce a certain variational form, which allows us to define a notion of viscosity solution. The uniqueness of viscosity solution is proved, and numerical nonlinear Gauss-Seidel method is constructed. Although the paper is devoted to the parabolic version of the two-phase obstacle-like problem, we prove convergence of discretized scheme to a unique viscosity solution for both two-phase parabolic obstacle-like and standard two-phase membrane problem. Numerical simulations are also presented.

  • 231.
    Arakelyan, Avetik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    The Finite Difference Methods for Multi-phase Free Boundary Problems2011Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis consist of an introduction and four research papers concerning numerical analysis for a certain class of free boundary problems.

    Paper I is devoted to the numerical analysis of the so-called two-phase membrane problem. Projected Gauss-Seidel method is constructed. We prove general convergence of the algorithm as well as obtain the error estimate for the finite difference scheme.

    In Paper II we have improved known results on the error estimates for a Classical Obstacle (One-Phase) Problem with a finite difference scheme.

    Paper III deals with the parabolic version of the two-phase obstacle-like problem. We introduce a certain variational form, which allows us to definea notion of viscosity solution. The uniqueness of viscosity solution is proved, and numerical nonlinear Gauss-Seidel method is constructed.

    In the last paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support. The proof of convergence of the numerical method is given in some particular cases. We also apply our numerical simulations for the spatial segregation limit of diffusive Lotka-Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions.

  • 232.
    Arakelyan, Avetik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Barkhudaryan, Rafayel
    Poghosyan, Mikayel
    Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference MethodManuskript (preprint) (Övrigt vetenskapligt)
  • 233.
    Arakelyan, Avetik
    et al.
    NAS Armenia, Inst Math, Yerevan 0019, Armenia..
    Barkhudaryan, Rafayel
    Amer Univ Armenia, Inst Math, NAS Armenia, Yerevan 0019, Armenia..
    Shahgholian, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Salehi, Mohammad
    Qatar Univ, Dept Math Stat & Phys, POB 2713, Doha, Qatar..
    Numerical Treatment to a Non-local Parabolic Free Boundary Problem Arising in Financial Bubbles2019Ingår i: Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, E-ISSN 1017-060X, Vol. 45, nr 1, s. 59-73Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic obstacle problems at each step to be solved, that in turn gives the next obstacle function in the iteration. The convergence of the proposed algorithm is proved. Moreover, we consider the finite difference scheme for this algorithm and obtain its convergence. At the end of the paper, we present and discuss computational results.

  • 234.
    Arakelyan, Avetik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Barkhydaryan, R.
    Poghosyan, Mikayel
    An Error Estimate for the Finite Difference Scheme for One-Phase Obstacle Problem2011Ingår i: Journal of Contemporary Mathematical Analysis, ISSN 1068-3623, Vol. 46, nr 3, s. 131-141Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider the finite difference scheme approximation for one-phase obstacle problem and obtain an error estimate for this approximation.

  • 235.
    Arakelyan, Avetik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Bozorgnia, Farid
    Numerical Algorithms for a Variational problem of the Spatial Segregation of Reaction-diffusion SystemsArtikel i tidskrift (Övrigt vetenskapligt)
  • 236. Araujo-Cabarcas, J. C.
    et al.
    Engström, C.
    Jarlebring, Elias
    KTH, Centra, SeRC - Swedish e-Science Research Centre. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map2018Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 330, s. 177-192Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances. 

  • 237.
    Arbegard, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Inflyttning i Stockholmsområdet - En regressionsanalys av variabler som påverkar inflyttningen i Stockholmskommunerna.2012Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Undersökningen handlade om att ta fram en modell med variabler för att avgöra om det finns några variabler som påverkar inflyttningen till en kommun i Stockholmsområdet och i så fall vilka dessa är.

    Undersökningen gjordes med hjälp av regressionsanalys av variablerna och metoden som användes var stepwise regression.

    På så sätt erhölls koefficienterna till modellen och med hjälp utav dessa kunde man tolka om variablerna hade positiv eller negativ inverkan samt testa huruvida väntevärdet skulle kunna vara negativt eller positivt med hjälp av hypotestest med konfidensintervall.

    Vid tolkning av variablerna så erhöll man att dem flesta variablerna betedde sig enligt dem hypoteserna man slagit fast vid tidigare.

    Det visade sig att dem flesta utav variablernas väntevärde vid 95% konfidens intervall faktiskt låg inom ett område där det kunde anta både positivt och negativt tecken.

    Dessutom gjordes residualplottar för att undersöka hur bra modellen var och om det förekom några mönster i variansen, det slogs fast vid observation att inga mönster förekom i plottarna.

    Slutsatsen man kom fram till att även om vissa variabler betedde sig enligt dem uppskattade hypoteserna så tar modellen inte hänsyn till en del faktorer som kan ändra inflyttningen, samt att det finns fler variabler som kan ha större betydelse för hur folk väljer sin hemkommun.

  • 238. Are, Sasanka
    et al.
    Katsoulakis, Markos A.
    Szepessy, Anders
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Coarse-Grained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles2009Ingår i: Chinese Annals of Mathematics. Series B, ISSN 0252-9599, E-ISSN 1860-6261, Vol. 30, nr 6, s. 653-682Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes such as the diffusion of interacting paxticles oil a surface, at a detailed atomistic level. However such algorithms are typically computationally expensive and are restricted to fairly small spatiotemporal scales. One approach towards overcoming this problem was the development of coarse-gained Monte Carlo algorithms. In recent literature, these methods were shown to be capable of efficiently describing much larger length scales while still incorporating information on microscopic interactions and fluctuations. In this paper, a coarse-grained Langevin system of stochastic differential equations as approximations of diffusion of interacting particles is derived, based on these earlier coarse-grained models. The authors demonstrate the asymptotic equivalence of transient and long time behavior of the Langevin approximation and the underlying microscopic process, using asymptotics methods such as large deviations for interacting particles systems, and furthermore, present corresponding numerical simulations, comparing statistical quantities like mean paths, auto correlations and power spectra of the microscopic and the approximating Langevin processes. Finally, it is shown that the Langevin approximations presented here are much more computationally efficient than conventional Kinetic Monte Carlo methods, since in addition to the reduction in the number of spatial degrees of freedom in coarse-grained Monte Carlo methods, the Langevin system of stochastic differential equations allows for multiple particle moves in a single timestep.

  • 239. Ariel, G.
    et al.
    Kim, S. J.
    Tsai, Richard
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Numerisk analys, NA.
    Parareal multiscale methods for highly oscillatory dynamical systems2016Ingår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, nr 6, s. A3540-A3564Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an appropriate multiscale integrator, which is refined using parallel fine scale integrations. Convergence is obtained using an alignment algorithm for fast phase-like variables. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances. We propose an alignment algorithm for almost-periodic solutions, in which case convergence of the parareal iterations is proved. The applicability of the method is demonstrated in numerical examples.

  • 240.
    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.

  • 241.
    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.

  • 242. 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.

  • 243.
    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..

  • 244.
    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

  • 245. 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.

  • 246.
    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.

  • 247.
    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

  • 248.
    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.

  • 249.
    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.

  • 250.
    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.

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