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Sökning: AMNE:(NATURVETENSKAP Matematik Beräkningsmatematik)

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  • Eriksson, Kimmo, et al. (författare)
  • Biases for acquiring information individually rather than socially
  • 2009
  • Ingår i: Journal of Evolutionary Psychology. - 0737-4828. ; 7:4, s. 309-329
  • Tidskriftsartikel (refereegranskat)abstract
    • We discuss theoretical and empirical arguments for a human bias to acquire information individually rather than socially. In particular, we argue that when other people can be observed, information collection is a public good and hence some of the individual variation in the choice between individual and social learning can be explained by variation in social value orientation. We conducted two experimental studies, based on the game Explore & Collect, to test the predictions that (1) socially and individually acquired information of equal objective value are treated differently, and (2) prosocial subjects tend to spend more effort than selfish subjects on individual acquiring of information. Both predictions were supported.
  • Eriksson, Kimmo, et al. (författare)
  • Partner Search Heuristics in the Lab: : Stability of Matchings Under Various Preference Structures
  • 2009
  • Ingår i: Adaptive Behavior. - 1059-7123 .- 1741-2633. ; 17:6, s. 524-536
  • Tidskriftsartikel (refereegranskat)abstract
    • When agents search for partners, the outcome is a matching. K. Eriksson and O. Häggström (2008) defined a measure of instability of matchings and proved that under a certain partner search heuristic, outcomes are likely to have low instability. They also showed that with regards to stability, the preference structure known as common preferences lie somewhere in between the extreme cases of homotypic and antithetical preferences. Following up on this theoretical work, we let human subjects search for a good partner in a computer game where preferences were set to be either common, homotypic, or antithetical. We find that total search effort and instability of the outcome vary in the predicted ways with the preference structure and the number of agents. A set of simulations show that these results are consistent with a model where agents use a simple search heuristic with a slight possibility of error.
  • Ni, Ying, 1976- (författare)
  • Nonlinearly Perturbed Renewal Equation with Perturbations of a Non-polynomial Type
  • 2010
  • Ingår i: Proceedings of the International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management, Beer Sheva, 2010.. - Beer Sheva : SCE - Shamoon College of Engineering. ; , s. 754-763
  • Konferensbidrag (refereegranskat)abstract
    • The object of study is a model of nonlinearly perturbed continuous-time renewal equation with multivariate non-polynomial perturbations. The characteristics of the distribution generating the renewal equation are assumed to have expansions in the perturbation parameter with respect to a non-polynomial asymptotic scale which can be considered as a generalization of the standard polynomial scale. Exponential asymptotics for such a model are obtained and applications are given.
  • Kurujyibwami, Celestin (författare)
  • Admissible transformations and the group classification of Schrödinger equations
  • 2017
  • Doktorsavhandling (övrigt vetenskapligt)abstract
    • We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. The first is the construction of the new theory of uniform seminormalized classes of differential equations and its application to solving group classification problems for these classes. Point transformations connecting two equations (source and target) from the class under study may have special properties of semi-normalization. This makes the group classification of that class using the algebraic method more involved. To extend this method we introduce the new notion of uniformly semi-normalized classes. Various types of uniform semi-normalization are studied: with respect to the corresponding equivalence group, with respect to a proper subgroup of the equivalence group as well as the corresponding types of weak uniform semi-normalization. An important kind of uniform semi-normalization is given by classes of homogeneous linear differential equations, which we call uniform semi-normalization with respect to linear superposition of solutions.The class of linear Schrödinger equations with complex potentials is of this type and its group classification can be effectively carried out within the framework of the uniform semi-normalization. Computing the equivalence groupoid and the equivalence group of this class, we show that it is uniformly seminormalized with respect to linear superposition of solutions. This allow us to apply the version of the algebraic method for uniformly semi-normalized classes and to reduce the group classification of this class to the classification of appropriate subalgebras of its equivalence algebra. To single out the classification cases, integers that are invariant under equivalence transformations are introduced. The complete group classification of linear Schrödinger equations is carried out for the cases n = 1 and n = 2.The second aim is to study group classification problem for classes of generalized nonlinear Schrödinger equations which are not uniformly semi-normalized. We find their equivalence groupoids and their equivalence groups and then conclude whether these classes are normalized or not. The most appealing classes are the class of nonlinear Schrödinger equations with potentials and modular nonlinearities and the class of generalized Schrödinger equations with complex-valued and, in general, coefficients of Laplacian term. Both these classes are not normalized. The first is partitioned into an infinite number of disjoint normalized subclasses of three kinds: logarithmic nonlinearity, power nonlinearity and general modular nonlinearity. The properties of the Lie invariance algebras of equations from each subclass are studied for arbitrary space dimension n, and the complete group classification is carried out for each subclass in dimension (1+2). The second class is successively reduced into subclasses until we reach the subclass of (1+1)-dimensional linear Schrödinger equations with variable mass, which also turns out to be non-normalized. We prove that this class is mapped by a family of point transformations to the class of (1+1)-dimensional linear Schrödinger equations with unique constant mass.
  • Araujo-Cabarcas, Juan Carlos, et al. (författare)
  • On spurious solutions in finite element approximations of resonances in open systems
  • 2017
  • Ingår i: ; 74:10, s. 2385-2402
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann–Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.
  • Engström, Christian (författare)
  • Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations
  • 2014
  • Ingår i: Numerische Mathematik. - : Springer. - 0029-599X .- 0945-3245. ; 126:3, s. 413-440
  • Tidskriftsartikel (refereegranskat)abstract
    • Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p -version and the h -version of the finite element method confirm the theoretical convergence rates.
  • Johnson, Tomas, 1979-, et al. (författare)
  • On a computer-aided approach to the computation of Abelian integrals
  • 2011
  • Ingår i: BIT Numerical Mathematics. - 0006-3835 .- 1572-9125. ; 51:3, s. 653-667
  • Tidskriftsartikel (refereegranskat)abstract
    • An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four.
  • Andersson, Anders (författare)
  • On the curvature of an inner curve in a Schwarz-Christoffel mapping
  • 2007
  • Rapport (övrigt vetenskapligt)abstract
    • In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-­Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded. In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-­Christoffel mapping from R, the unit disk or upper half­plane, to a polygonal region P of a curve inside R. From the Schwarz-­Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.
  • Al-Talibi, Haidar (författare)
  • Nelson-type Limits for α-Stable Lévy Processes
  • 2010
  • Licentiatavhandling (övrigt vetenskapligt)abstract
    • Brownian motion has met growing interest in mathematics, physics and particularly in finance since it was introduced in the beginning of the twentieth century. Stochastic processes generalizing Brownian motion have influenced many research fields theoretically and practically. Moreover, along with more refined techniques in measure theory and functional analysis more stochastic processes were constructed and studied. Lévy processes, with Brownian motionas a special case, have been of major interest in the recent decades. In addition, Lévy processes include a number of other important processes as special cases like Poisson processes and subordinators. They are also related to stable processes. In this thesis we generalize a result by S. Chandrasekhar [2] and Edward Nelson who gave a detailed proof of this result in his book in 1967 [12]. In Nelson’s first result standard Ornstein-Uhlenbeck processes are studied. Physically this describes free particles performing a random and irregular movement in water caused by collisions with the water molecules. In a further step he introduces a nonlinear drift in the position variable, i.e. he studies the case when these particles are exposed to an external field of force in physical terms. In this report, we aim to generalize the result of Edward Nelson to the case of α-stable Lévy processes. In other words we replace the driving noise of a standard Ornstein-Uhlenbeck process by an α-stable Lévy noise and introduce a scaling parameter uniformly in front of all vector fields in the cotangent space, even in front of the noise. This corresponds to time being sent to infinity. With Chandrasekhar’s and Nelson’s choice of the diffusion constant the stationary state of the velocity process (which is approached as time tends to infinity) is the Boltzmann distribution of statistical mechanics.The scaling limits we obtain in the absence and presence of a nonlinear drift term by using the scaling property of the characteristic functions and time change, can be extended to other types of processes rather than α-stable Lévy processes. In future, we will consider to generalize this one dimensional result to Euclidean space of arbitrary finite dimension. A challenging task is to consider the geodesic flow on the cotangent bundle of a Riemannian manifold with scaled drift and scaled Lévy noise. Geometrically the Ornstein-Uhlenbeck process is defined on the tangent bundle of the real line and the driving Lévy noise is defined on the cotangent space.
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