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  • 201.
    Hultman, Axel
    KTH, Superseded Departments, Mathematics.
    Polygraph arrangements2002In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 23, no 8, p. 937-948Article in journal (Refereed)
    Abstract [en]

    A class of subspace arrangements, Z(n, m), known as polygraph arrangements was exploited by Haiman in order to prove the n! theorem. By showing that their intersection lattices, L(Z(n, m)), are EL-shellable, we determine the cohomology groups of the complements of the arrangements. Moreover, we generalize the shellability results to a class of lattices which deserve to be called Dowling generalizations of L (Z (n, m)). As a consequence, we obtain the cohomology groups of the complements of certain Dowling analogues of polygraph arrangements.

  • 202.
    Hultman, Axel
    KTH, Superseded Departments, Mathematics.
    Quotient complexes and lexicographic shellability2002In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 16, no 1, p. 83-96Article in journal (Refereed)
    Abstract [en]

    Let Pi(n,k,k) and Pi(n,k,h), h < k, denote the intersection lattices of the k-equal subspace arrangement of type D-n and the k, h-equal subspace arrangement of type B-n respectively. Denote by S-n(B) the group of signed permutations. We show that Delta(Pi(n,k,k))/S-n(B) is collapsible. For Delta(Pi(n,k,h))/S-n(B),h < k, we show the following. If n = 0 (mod k), then it is homotopy equivalent to a sphere of dimension 2n/k = 2. If n = h (mod k), then it is homotopy equivalent to a sphere of dimension 2n-h/k-1. Otherwise, it is contractible. Immediate consequences for the multiplicity of the trivial characters in the representations of S-n(B) on the homology groups of Delta(Pi(n,k,k)) and Delta(Pi(n,k,h)) are stated. The collapsibility of Delta (Pi(n,k,k))/S-n(B) is established using a discrete Morse function. The same method is used to show that Delta(Pi(n,k,h))/S-n(B), h < k, is homotopy equivalent to a certain subcomplex. The homotopy type of this subcomplex is calculated by showing that it is shellable. To do this, we are led to introduce a lexicographic shelling condition for balanced cell complexes of boolean type. This extends to the non-pure case work of P. Hersh (Preprint, 2001) and specializes to the CL-shellability of A. Bjorner and M. Wachs (Trans. Amer. Math. Soc. 4 (1996), 1299-1327) when the cell complex is an order complex of a poset.

  • 203. Hundertmark, D.
    et al.
    Laptev, Ari
    KTH, Superseded Departments, Mathematics.
    Weidl, T.
    New bounds on the Lieb-Thirring constants2000In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 140, no 3, p. 693-704Article in journal (Refereed)
    Abstract [en]

    Improved estimates on the constants L(gamma,)d, foT 1/2 < gamma < 3/2, d epsilon N, in the inequalities for the eigenvalue moments of Schrodinger operators are established.

  • 204.
    Håstad, Johan
    KTH, Superseded Departments, Mathematics.
    On bounded occurrence constraint satisfaction2000In: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 74, no 02-jan, p. 1-6Article in journal (Refereed)
    Abstract [en]

    An approximation algorithm for a constraint satisfaction problem is said to be nontrivial if its performance ratio is strictly superior to the expected performance of the algorithm which simply chooses a random assignment. We prove that any constraint satisfaction problem where each variable appears a bounded number of times admits a nontrivial polynomial time approximation algorithm.

  • 205. Ianelli, L.
    et al.
    Johansson, Karl Henrik
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Vasca, F.
    Analysis of dither in relay feedback systems2002In: PROCEEDINGS OF THE 41ST IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, IEEE , 2002, p. 4425-4430Conference paper (Refereed)
    Abstract [en]

    Dither signals provide an effective way of compensating for nonlinearities in control systems. The seminal, works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. This paper presents initial results on how to analyze and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system obtained through an averaging approach. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system.

  • 206. Ianelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Vasca, F.
    Practical stability and limit cycles of dithered relay feedback systems2003Conference paper (Refereed)
    Abstract [en]

    A new constructive way for choosing dither amplitude and frequency in order to effectively stabilize relay feedback systems by triangular dither is proposed. It is argued that the proposed averaging approach is not easily extended to square dither signals. Trajectories composed by smooth and switching parts are also analyzed and their relationship with limit cycles exhibited by the smoothed system is investigated.

  • 207. Ianelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Vasca, Francesco
    Dither shape in the averaging of switched systems2004In: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, IEEE , 2004, p. 5812-5817Conference paper (Refereed)
    Abstract [en]

    It was shown by Zames and Shneydor that a high-frequency dither of a quite arbitrary shape can be used to smooth the effective nonlinear sector of Lipschitz continuous feedback systems. Here it is shown that also systems with discontinuous nonlinearities can be smoothed using dither signals, as long as the amplitude distribution function of the dither is Lipschitz continuous.

  • 208. Ianelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Vasca, Francesco
    Effects of dither shapes in nonsmooth feedback systems: experimental results and theoretical insight2003In: Proceedings of the 42nd IEEE Conference on Decision and Control, Vols. 1-6, IEEE , 2003, p. 4285-4290Conference paper (Refereed)
    Abstract [en]

     Dither signals are commonly used to compensate for nonlinearities in feedback systems in electronics and mechanics. Recently, theoretical results were proposed for the analysis or a particularly interesting class of nonsmooth systems, namely relay feedback systems with triangular dither. In this paper the class of dither signals is enlarged by considering square and trapezoidal dither: it is shown how the dither shape affects the behavior of nonsmooth feedback systems, differently from the case of dither in Lipschitz continuous systems. Experimental results support this fact and a theoretical insight is given in order to explain the phenomena.

  • 209. Iannelli, L.
    et al.
    Johansson, K. H.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    Vasca, F.
    Analysis of periodically forced uncertain feedback systems2003In: IEEE Transactions on Circuits And Systems Part I: Fundamental Theory and Applications, ISSN 1057-7122, E-ISSN 1558-1268, Vol. 50, no 2, p. 244-258Article in journal (Refereed)
    Abstract [en]

    Conditions for existence and stability of stationary periodic solutions of uncertain periodic systems are addressed in this paper. Existence and harmonic performance are studied using integral quadratic constraints (IQCs) defined on the space of square integrable periodic functions. Stability is investigated using IQCs defined on the usual space of square integrable functions. The analysis results in criteria formulated as affinely parameterized operator inequalities. Methods of convex optimization are used to find feasible parameters. Two applications will be discussed. The first is harmonic analysis of an electronic circuit and the second involves estimation of the amplitude of a periodic disturbance in a nonlinear control system.

  • 210. Ibragimov, N. H.
    et al.
    Kolsrud, Torbjörn
    KTH, Superseded Departments, Mathematics.
    Lagrangian approach to evolution equations: Symmetries and conservation laws2004In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, no 1, p. 29-40Article in journal (Refereed)
    Abstract [en]

    We show that one can apply a Lagrangian approach to certain evolution equations by considering them together with their associated equations. Consequently, one can employ Noether's theorem and derive conservation laws from symmetries of coupled systems of evolution equations. We discuss in detail the linear and non-linear heat equations as well as the Burgers equation and obtain new non-local conservation laws for the non-linear heat and the Burgers equations by extending their symmetries to the associated equations. We also provide Lagrangians for non-linear Schrodinger and Korteweg-de Vries type systems.

  • 211.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Determinantal processes with number variance saturation2004In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 252, no 3-Jan, p. 111-148Article in journal (Refereed)
  • 212.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Discrete orthogonal polynomial ensembles and the Plancherel measure2001In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 153, no 1, p. 259-296Article in journal (Refereed)
  • 213.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Discrete polynuclear growth and determinantal processes2003In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 242, no 2-Jan, p. 277-329Article in journal (Refereed)
  • 214.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Non-intersecting paths, random tilings and random matrices2002In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 123, no 2, p. 225-280Article in journal (Refereed)
  • 215.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Shape fluctuations and random matrices2000In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 209, no 2, p. 437-476Article in journal (Refereed)
  • 216.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Transversal fluctuations for increasing subsequences on the plane2000In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 116, no 4, p. 445-456Article in journal (Refereed)
  • 217.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices2001In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 215, no 3, p. 683-705Article in journal (Refereed)
  • 218.
    Jonsson, Mattias
    KTH, Superseded Departments, Mathematics.
    Dynamical studies in several complex variables1997Doctoral thesis, comprehensive summary (Other scientific)
  • 219.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Local robustness of oscillator networks2004In: 2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, p. 4649-4654Conference paper (Refereed)
    Abstract [en]

    Conditions for robust stability of networks of identical coupled oscillators are derived. Local stability as well as the computation of a robustness margin is considered.

  • 220.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    A cutting plane algorithm for robustness analysis of periodically time-varying systems2001In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 46, no 4, p. 579-592Article in journal (Refereed)
    Abstract [en]

    An algorithm for robustness analysis of periodic systems is derived. The system under consideration consists of a linear periodically time-varying plant in feedback interconnection with a structured uncertainty, Conditions for robust stability and robust performance can be formulated in terms of periodic integral quadratic constraints (IQCs), in this way, the robustness analysis becomes a problem of optimizing the parameters of the IQC. A cutting plane algorithm is suggested for solving this infinite-dimensional optimization problem.

  • 221.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    New results for analysis of systems with repeated nonlinearities2001In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 37, no 5, p. 739-747Article in journal (Refereed)
    Abstract [en]

    This work presents new results for analysis of systems with repeated monotonic or slope restricted nonlinearities. We first give new integral quadratic constraints (IQCs) that are satisfied by the inputs and outputs of diagonal operators with equal, monotonic or slope restricted, diagonal entries. Then, we present new analysis results For systems with repeated nonlinearities, obtained using the new IQCs. For the type of nonlinearities considered in this work, the new results are less conservative than previously known results. The computation of the new conditions is discussed. The results in this paper apply also to problems with nonrepeated nonlinearities whenever these are representable as the interconnection of multiple repeated nonlinearities and a constant matrix.

  • 222.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    Robustness of periodic trajectories2002In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 47, no 11, p. 1842-1856Article in journal (Refereed)
    Abstract [en]

    A robustness problem for periodic trajectories is considered in this paper. A nonautonomous system with a periodic solution is given. The problem is to decide whether a stable periodic solution remains in a neighborhood of the nominal periodic solution when, the dynamics of the system is perturbed. The case with a structured dynamic perturbation is considered. This makes the problem a nontrivial generalization of a classical problem in the theory of dynamical systems. A solution to the robustness problem will be obtained by using a variational system obtained by linearizing the system dynamics along a trajectory, which is uncertain but within the prespecified neighborhood of the nominal trajectory. This gives rise to robustness conditions that can be solved using integral quadratic constraints for linear time periodic systems.

  • 223.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    Trajectory planning for systems with a multiplicative stochastic uncertainty2004In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 77, no 8, p. 713-722Article in journal (Refereed)
    Abstract [en]

    A trajectory planning problem for linear stochastic differential equations is considered in this paper. The aim is to control the system such that the expected value of the output interpolates given points at given times while the variance and an integral cost of the control effort are minimized. The solution is obtained by using the dynamic programming technique, which allows for several possible generalizations. The results of this paper can be used for control of systems with a multiplicative stochastic disturbance on the state vector and systems with a stochastic growth rate. This is frequently the case in investment problems, biomathematics and control theory.

  • 224.
    Kaario, Katja
    et al.
    Department of Mathematical Information Technology, University of Jyväskylä.
    Miettinen, Kaisa
    KTH, Superseded Departments, Mathematics.
    Mäkelä, Marko M.
    Department of Mathematical Information Technology, University of Jyväskylä.
    Saariluoma, P.
    Symbolic and Graphic Classification in Interactive Multiobjective Optimization System WWW-NIMBUS2004In: CD-Proceedings of 4th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS2004, Volume II / [ed] Neittaanmäki, P., Rossi, T., Korotov, S., Onate, E., Periaux, J., Knörzer, D., 2004Conference paper (Refereed)
  • 225.
    Kao, ChungYao
    et al.
    KTH, Superseded Departments, Mathematics.
    Lincoln, B
    Simple stability criteria for systems with time-varying delays2004In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 40, no 8, p. 1429-1434Article in journal (Refereed)
    Abstract [en]

    This paper considers the problem of checking stability of linear feedback systems with time-varying but bounded delays. Simple but powerful criteria of stability are presented for both continuous-time and discrete-time systems. Using these criteria, stability can be checked in a closed loop Bode plot. This makes it easy to design the system for robustness.

  • 226.
    Kao, Chung-Yao
    et al.
    KTH, Superseded Departments, Mathematics.
    Megretski, A.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    Specialized fast algorithms for IQC feasibility and optimization problems2004In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 40, no 2, p. 239-252Article in journal (Refereed)
    Abstract [en]

    The conventional way to treat integral quadratic constraint (IQC) problems is to transform them into semi-definite programs (SDPs). SDPs can then be solved using interior point methods which have been proven efficient. This approach, however, is not always the most efficient since it introduces additional decision variables to the SDP, and the additional decision variables sometimes largely increase the complexity of the problem. In this paper, we demonstrate how to solve IQC problems by other alternatives. More specifically, we consider two cutting plane algorithms. We will show that in certain cases these cutting plane algorithms can solve IQC problems much faster than the conventional approach. Numerical examples, as well as some explanations from the point of view of computational complexity, are provided to support our point.

  • 227.
    Kao, Chung-Yao
    et al.
    KTH, Superseded Departments, Mathematics.
    Megretski, A.
    Jönsson, Ulf T.
    KTH, Superseded Departments, Mathematics.
    Rantzer, A.
    A MATLAB toolbox for robustness analysis2004In: Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, 2004, p. 297-302Conference paper (Refereed)
    Abstract [en]

    Verification of control systems is often done using extensive simulation. This gives the engineer useful qualitative information about the system performance. However, simulation cannot be used to rigorously prove stability and robustness of the system. Such properties can only be verified using mathematical analysis which for many realistic systems becomes rather involved. This paper presents the MATLAB toolbox IQCβ. It provides a user friendly interface for advanced semi-automatic systems analysis.

  • 228.
    Karakhanyan, Aram
    KTH, Superseded Departments, Mathematics.
    Existence and regularity of free boundary problems with fixed gradient condition2004Doctoral thesis, comprehensive summary (Other scientific)
  • 229.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Free subgroups of groups with nontrivial Floyd boundary2003In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 31, no 11, p. 5361-5376Article in journal (Refereed)
    Abstract [en]

    We prove that when a countable group admits a nontrivial Floyd-type boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the corresponding well-known results for hyperbolic groups and groups with infinitely many ends. It also shows that no finitely generated amenable group admits a nontrivial boundary of this type. This improves on a theorem by Floyd (Floyd, W. J. (1980). Group completions and limit sets of Kleinian groups. Invent. Math. 57: 205-218) as well as giving an elementary proof of a conjecture stated in that same paper. We also show that if the Floyd boundary of a finitely generated group is nontrivial, then it is a boundary in the sense of Furstenberg and the group acts on it as a convergence group.

  • 230.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Linear rate of escape and convergence in direction2004In: Random Walks And Geometry / [ed] Kaimanovich, VA, BERLIN 30: WALTER DE GRUYTER & CO , 2004, p. 459-471Conference paper (Refereed)
    Abstract [en]

    This paper describes some situations when random walks (or related processes) of linear rate of escape converge in direction in various senses. We discuss random walks on isometry groups of fairly general metric spaces, and more specifically, random walks on isometry groups of nonpositive curvature, isometry groups of reflexive Banach spaces, and linear groups preserving a proper cone. We give an alternative proof of the main tool from subadditive ergodic theory and we make a conjecture in this context involving Busemann functions.

  • 231.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Non-expanding maps and Busemann functions2001In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 21, p. 1447-1457Article in journal (Refereed)
    Abstract [en]

    We give stronger versions and alternative simple proofs of some results of Beardon, [Be1] and [Be2]. These results concern contractions of locally compact metric spaces and generalize the theorems of Wolff and Denjoy about the iteration of a holomorphic map of the unit disk. In the case of unbounded orbits, there are two types of statements which can sometimes be proven; first, about invariant horoballs, and second, about the convergence of the iterates to a point on the boundary. A few further remarks of similar type are made concerning certain random products of sernicontractions and also concerning semicontractions of Gromov hyperbolic spaces.

  • 232.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Semicontraction, Nonpositive Curvature, and Multiplicative Ergodic Theory2000Doctoral thesis, monograph (Other scientific)
  • 233.
    Karlsson, Anders
    et al.
    KTH, Superseded Departments, Mathematics.
    Noskov, G. A.
    Some groups having only elementary actions on metric spaces with hyperbolic boundaries2004In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 104, no 1, p. 119-137Article in journal (Refereed)
    Abstract [en]

    We study isometric actions of certain groups on metric spaces with hyperbolic-type bordifications. The class of groups considered includes SLn(Z), Artin braid groups and mapping class groups of surfaces (except the lower rank ones). We prove that in various ways such actions must be elementary. Most of our results hold for non-locally compact spaces and extend what is known for actions on proper CAT(- 1) and Gromov hyperbolic spaces. We also show that SLn(Z) for ngreater than or equal to3 cannot act on a visibility space X without. xing a point in (X) over bar. Corollaries concern Floyd's group completion, linear actions on strictly convex cones, and metrics on the moduli spaces of compact Riemann surfaces. Some remarks on bounded generation are also included.

  • 234.
    Karlsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Semi-classical approximations of Quantum Mechanical problems2002Doctoral thesis, comprehensive summary (Other scientific)
  • 235. Karp, L.
    et al.
    Kilpelainen, T.
    Petrosyan, A.
    Shahgholian, Henrik.
    KTH, Superseded Departments, Mathematics.
    On the porosity of free boundaries in degenerate variational inequalities2000In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 164, no 1, p. 110-117Article in journal (Refereed)
    Abstract [en]

    In this note we consider a certain degenerate variational problem with constraint identically zero. The exact growth of the solution near th free boundary is established. A consequence of this is that the free boundary is porous and therefore its Hausdorff dimension is less than N and hence it is of Lebesgue measure zero.

  • 236. Karp, L.
    et al.
    Shahgholian, Henrik.
    KTH, Superseded Departments, Mathematics.
    Regularity of a free boundary at the infinity point2000In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 25, no 12-Nov, p. 2055-2086Article in journal (Refereed)
    Abstract [en]

    Suppose there is a nonnegative function u and an open set Ohm subset of R-n(n greater than or equal to 3), satisfying Deltau = chi (Ohm) in B-r(e), u = \delu\ = 0 on B-r(e)\Ohm, where B-r(e) = {x : \x\ > r}. Under a certain thickness condition on R-n\Ohm, we prove that the boundary of {x:x/\x\(2) is an element of Ohm} is a graph of a C-1 function in a neighborhood of the origin. As a by-product of the method of the proof, we also obtain the following result: Replace chi (Ohm) by f chi (Ohm), with a certain assumptions on f. Then for any solution u which is asymptotically nonnegative at infinity, there holds lim(r-->infinity) (\Br\)/(\Ohm boolean AND Br\) is an element of {1/2,1}.

  • 237.
    Kolsrud, Torbjörn
    et al.
    KTH, Superseded Departments, Mathematics.
    Loubeau, E.
    Foliated manifolds and conformal heat morphisms2002In: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 21, no 3, p. 241-267Article in journal (Refereed)
    Abstract [en]

    The objects under study, in this article, are Riemannian manifolds foliated by hypersurfaces. Looking at the transverse direction as time, we construct the generalised heat operator and, in the spirit of a time-space extension of harmonic morphisms, we introduce the conformal heat morphisms. Concrete examples of these concepts are presented, as well as, a characterisation of conformal heat morphisms. Lastly, we calculate the heat Lie algebra of the generalised heat operator.

  • 238.
    Koski, Timo
    KTH, Superseded Departments, Mathematics.
    Hidden Markov Models for Bioinformatics2001Book (Refereed)
  • 239.
    Koski, Timo
    KTH, Superseded Departments, Mathematics.
    Minimizing stochastic complexity using local search and GLA with applications to classification of bacteria2000In: Biosystems (Amsterdam. Print), ISSN 0303-2647, E-ISSN 1872-8324, Vol. 57, no 1, p. 37-48Article in journal (Refereed)
    Abstract [en]

    In this paper, we compare the performance of two iterative clustering methods when applied to an extensive data set describing strains of the bacterial family Enterobacteriaceae. In both methods, the classification (i.e. the number of classes and the partitioning) is determined by minimizing stochastic complexity. The first method performs the minimization by repeated application of the generalized Lloyd algorithm (GLA). The second method uses an optimization technique known as local search (LS). The method modifies the current solution by making global changes to the class structure and it, then, performs local fine-tuning to find a local optimum. II is observed that if we fix the number of classes, the LS finds a classification with a lower stochastic complexity value than GLA. In addition, the valiance of the solutions is much smaller for the LS due to its more systematic method of searching. Overall, the two algorithms produce similar classifications but they merge cel tain natural classes with microbiological relevance in different ways.

  • 240.
    Kozlov, Dimitrij
    KTH, Superseded Departments, Mathematics.
    Directed trees in a string, real polynomials with triple roots, and chain mails2004In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 32, no 3, p. 373-382Article in journal (Refereed)
    Abstract [en]

    This paper starts with an observation that two infinite series of simplicial complexes, which a priori do not seem to have anything to do with each other, have the same homotopy type. One series consists of the complexes of directed forests on a double directed string, while the other one consists of Shapiro-Welker models for the spaces of hyperbolic polynomials with a triple root. We explain this coincidence in the more general context by finding an explicit homotopy equivalence between complexes of directed forests on a double directed tree, and doubly disconnecting complexes of a tree.

  • 241.
    Kuroiwa, Yohei
    et al.
    KTH, Superseded Departments, Mathematics.
    Kimura, Hidenori
    H-infinity control with preview and delay2004In: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, p. 4794-4799Conference paper (Refereed)
    Abstract [en]

    An H-infinity control problem with simultaneous consideration of preview and delay is solved, where past signals and future signals are essential to describe. behaviors of the control system. Solvability conditions and complete controller parameterization are derived in the frequency domain within the scope of finite dimensional computations, that is, infinite dimensional aspects attributed to preview and delay are transformed to equivalent finite dimensional problems. The two-degree-of-freedom version is also considered.

  • 242.
    Laksov, Dan
    KTH, Superseded Departments, Mathematics.
    Local and global structure of effective and cuspidal loci on Grassmannians2003In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 31, no 8, p. 3993-4006Article in journal (Refereed)
    Abstract [en]

    We introduce effective loci, which are central for the study of differential systems, in a very general setting. The greater generality makes them useful in a wider range of situations; and it also makes their study more straightforward, and convenient technically. Our treatment of effective loci is based on families of relative tangents. Such families give rise, in natural ways, to Semple sheaves, and hence allow us to construct the higher contact loci by straightforward iteration. Our main result is a local description of generic effective loci, on key Grassmannians for geometric applications. We show, by means of very natural frames, that these effective loci are precisely where certain generic matrices become symmetric.

  • 243.
    Laksov, Dan
    KTH, Superseded Departments, Mathematics.
    The algebra of jets2000In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 48, p. 393-416Article in journal (Refereed)
  • 244.
    Laksov, Dan
    KTH, Superseded Departments, Mathematics.
    Wronski systems for families of local complete intersection curves2003In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 31, no 8, p. 4007-4035Article in journal (Refereed)
    Abstract [en]

    We construct a substitute for principal parts for systems of algebras with a natural local presentation by free modules. The main application of the theory is to families of locally complete intersection curves. In that case we obtain the sheaves of E steves. The advantage of the greater generality is that it makes the theory much more transparent. It also makes it possible to avoid many technical difficulties.

  • 245.
    Laksov, Dan
    et al.
    KTH, Superseded Departments, Mathematics.
    Ekedahl, Torsten
    Two "generic" proofs of the spectral mapping theorem2004In: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 111, no 7, p. 572-585Article in journal (Refereed)
  • 246.
    Laksov, Dan
    et al.
    KTH, Superseded Departments, Mathematics.
    Pitteloud, Y.
    Skjelnes, Roy Mikael
    KTH, Superseded Departments, Mathematics.
    Notes on flatness and the Quot functor on rings2000In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 28, no 12, p. 5613-5627Article in journal (Refereed)
    Abstract [en]

    For Rat modules M over a ring A we study the similarities between the three statements, dim(kappa (P))(kappa (P) circle times (A) M) = d far all prime ideals P of A, the A(P)-module Mp is free of rank d for all prime ideals P of A, and M is a locally free A-module of rank d. We have particularly emphasized the case when there is an A-algebra B, essentially of finite type, and M is a finitely generated B-module.

  • 247.
    Laksov, Dan
    et al.
    KTH, Superseded Departments, Mathematics.
    Skjelnes, Roy Mikael
    KTH, Superseded Departments, Mathematics.
    The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin2001In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 126, no 3, p. 323-334Article in journal (Refereed)
    Abstract [en]

    We introduce symmetrizing operators of the polynomial ring A[x] in the variable x over a ring A. When A is an algebra over a field k these operators are used to characterize the monic polynomials F(x) of degree n in A[x] such that Ax(k)k[x]((x))/(F(x)) is a free A-module of rank n. We use the characterization to determine the Hilbert scheme parameterizing subschemes of length n of k[x]((x)).

  • 248.
    Landen, Camilla
    KTH, Superseded Departments, Mathematics.
    Finite-dimensional Markovian realizations for stochastic volatility forward-rate models2004In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 460, no 2041, p. 53-83Article in journal (Refereed)
    Abstract [en]

    We consider forward-rate models of Heath-Jarrow-Morton type, as well as more general infinite-dimensional stochastic differential equations, where the volatility-diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework, we use the previously developed Hilbert-space-realization theory in order to provide general necessary and sufficient conditions for the existence of a finite-dimensional Markovian realization for the stochastic volatility models. We illustrate the theory by analysing a number of concrete examples.

  • 249.
    Landén, Camilla
    KTH, Superseded Departments, Mathematics.
    Bond pricing in a hidden Markov model of the short rate2000In: Finance and Stochastics, ISSN 0949-2984, E-ISSN 1432-1122, Vol. 4, no 4, p. 371-389Article in journal (Refereed)
    Abstract [en]

    We consider a diffusion type model for the short rate, where the drift and diffusion parameters are modulated by an underlying Markov process. The underlying Markov process is assumed to have a stochastic differential driven by Wiener processes and a marked point process. The model for the short rate thus falls within the category of hidden Markov models. For this model we look at the bond pricing problem. In order to obtain more concrete results we introduce the notion of a semi-affine term structure and give sufficient conditions for the existence of such a term structure. For a special case, when the underlying process is a Markov chain with only two states, we obtain a closed form expression for bond prices. Furthermore we consider the pricing problem when the modulating process can not be directly observed. It turns out that pricing in this context may be viewed as a filtering problem.

  • 250.
    Landén, Camilla
    KTH, Superseded Departments, Mathematics.
    On the term structure of forwards, futures and interest rates2001Doctoral thesis, comprehensive summary (Other scientific)
234567 201 - 250 of 334
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