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Sökning: FÖRF:(Tomas Johansson)

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1.
  • Baravdish, George, et al. (författare)
  • Identifying a response parameter in a model of brain tumour evolution under therapy
  • 2023
  • Ingår i: IMA Journal of Applied Mathematics. - : Oxford University Press. - 0272-4960 .- 1464-3634. ; 88:2, s. 378-404
  • Tidskriftsartikel (refereegranskat)abstract
    • A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction-diffusion type corresponding to the evolution of brain tumours under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative method is outlined as well as uniqueness of a solution to the inverse problem. Moreover, the parameter identification is recasted as the minimization of a Tikhonov type functional and the existence of a minimizer to this functional is shown. Finite-difference discretization of the space and time derivatives are employed for the numerical implementation. Numerical simulations on full 3D brain data are included showing that information about a spacewise-dependent treatment parameter can be recovered in a stable way.
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2.
  • Borachok, Ihor, et al. (författare)
  • Rothes method in combination with a fundamental sequences method for the nonstationary Stokes problem
  • 2023
  • Ingår i: Numerical Algorithms. - : SPRINGER. - 1017-1398 .- 1572-9265.
  • Tidskriftsartikel (refereegranskat)abstract
    • Rothes method combined with a fundamental sequences method is considered for the numerical solution of the nonstationary (unsteady) homogeneous Stokes problem in two-dimensional doubly connected domains. The Stokes system is reduced, using Rothes method, to a sequence of stationary inhomogeneous problems with a known sequence of fundamental solutions. The stationary problems are discretized by a fundamental sequences method; this means searching for the solution as a linear combination of elements of the fundamental sequence and matching the given boundary conditions in order to find the coefficients in the expansion of the solution. No additional reduction of the inhomogeneous problems is needed, making it an efficient method and different from standard strategies of the method of fundamental solutions. Results of numerical experiments are given, and these confirm the applicability of the proposed approach.
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3.
  • Jaroudi, Rym, 1989- (författare)
  • Inverse Problems for Tumour Growth Models and Neural ODEs
  • 2023
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis concerns the application of methods and techniques from the theory of inverse problems and differential equations to study models arising in the areas of mathematical oncology and deep learning. The first problem studied is to develop methods to perform numerical simulations with full 3-dimensional brain imaging data of reaction-diffusion models for tumour growth forwards as well as backwards in time with the goal of enabling the numerical reconstruction of the source of the tumour given an image (or similar data) at a later stage in time of the tumour. This inverse ill-posed problem is solved as a sequence of well-posed forward problems using the nonlinear Landweber regularization method. Such models and method allow to generate realistic synthetic medical images that can be used for data augmentation. Mathematical analysis of the problems solved as well as establishing uniqueness of the source are presented. The second problem includes a novel method allowing training self-contained neural ordinary differential equation networks (termed standalone NODEs) via a nonlinear conjugate gradient method, where the Sobolev gradient can be incorporated to improve smoothness of model weights. Relevant functions spaces are introduced, the adjoint problems with the needed gradients are calculated and the robustness is studied. The developed framework has many advantages in that it can incorporate relevant dynamics from physical models as well as help to understand more on how neural networks actually work and how sensitive they are to natural and adversarial perturbations. Combination of the two main problems will allow for example the training of neural networks to identify tumours in real imaging data. 
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4.
  • Molbert, Noëlie, et al. (författare)
  • An evaluation of DNA extraction methods on historical and roadkill mammalian specimen
  • 2023
  • Ingår i: Scientific Reports. - 2045-2322. ; 13
  • Tidskriftsartikel (refereegranskat)abstract
    • Guidelines identifying appropriate DNA extraction methods for both museum and modern biological samples are scarce or non-existent for mammalian species. Yet, obtaining large-scale genetic material collections are vital for conservation and management purposes. In this study, we evaluated five protocols making use of either spin-column, organic solvents, or magnetic bead-based methods for DNA extraction on skin samples from both modern, traffic-killed (n = 10) and museum (n = 10) samples of European hedgehogs, Ericaneus europaeus. We showed that phenol-chloroform or silica column (NucleoSpin Tissue) protocols yielded the highest amount of DNA with satisfactory purity compared with magnetic bead-based protocols, especially for museum samples. Furthermore, extractions using the silica column protocol appeared to produce longer DNA fragments on average than the other methods tested. Our investigation demonstrates that both commercial extraction kits and phenol-chloroform protocol retrieve acceptable DNA concentrations for downstream processes, from degraded remnants of traffic-killed and museum samples of mammalian specimens. Although all the tested methods could be applied depending on the research questions and laboratory conditions, commercial extraction kits may be preferred due to their effectiveness, safety and the higher quality of the DNA extractions.
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5.
  • Borachok, Ihor, et al. (författare)
  • A method of fundamental solutions for heat and wave propagation from lateral Cauchy data
  • 2022
  • Ingår i: Numerical Algorithms. - : SPRINGER. - 1017-1398 .- 1572-9265. ; 89:1, s. 431-449
  • Tidskriftsartikel (refereegranskat)abstract
    • We derive a method of fundamental solutions (MFS) for the numerical solution of an ill-posed lateral Cauchy problem for the hyperbolic wave equation in bounded planar annular domains. The Laguerre transform is applied to reduce the time-dependent lateral Cauchy problem to a sequence of elliptic Cauchy problems with a known set of fundamental solutions termed a fundamental sequence. The solution of the elliptic problems is approximated by linear combinations of the elements in the fundamental sequence. Source points are placed outside of the solution domain, and by collocating on the boundary of the solution domain itself a sequence of linear equations is obtained for finding the coefficients in the MFS approximation. It is shown that the fundamental solutions used constitute a linearly independent and dense set on the boundary of the solution domain with respect to the L-2-norm. Tikhonov regularization is applied to get a stable solution to the obtained systems of linear equations in combination with the L-curve rule for selecting the regularization parameter. Numerical results confirm the efficiency and applicability of the proposed strategy for the considered lateral Cauchy problem both in the case of exact and noisy data. Adjusting the coefficients in the sequence of elliptic equations, the similar strategy and results apply also to the parabolic lateral Cauchy problem as verified by an included numerical example. It is also shown that by adjusting the coefficients further the method of Rothe can be applied as an alternative to the Laguerre transformation in time.
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6.
  • Borachok, Ihor, et al. (författare)
  • An inverse elastodynamic data reconstruction problem
  • 2022
  • Ingår i: Journal of Engineering Mathematics. - Dordrecht, Netherlands : Springer. - 0022-0833 .- 1573-2703. ; 134:1
  • Tidskriftsartikel (refereegranskat)abstract
    • A method of fundamental solutions (MFS) is presented for the ill-posed linear inverse problem consisting of the reconstruction of boundary data on the inner boundary for the hyperbolic system of elastodynamics in planar annular domains from known essential and natural boundary conditions on the outer boundary. This corresponds to the problem of finding elastic wave propagation in a structure from measured data being the displacement and traction on a portion of the boundary of the structure. The time-dependent lateral Cauchy problem is reduced to a sequence of elliptic systems by applying the Laguerre transform. A sequence of fundamental solutions to the elliptic equations are derived. Linear combination of elements of this sequence of fundamental solutions is used to generate an approximation to the elliptic Cauchy problems. By placing source points outside of the solution domain, and collocating on the boundary, linear equations are obtained for finding the coefficients in the MFS approximation. It is outlined that the sequence of fundamental solutions of the elliptic systems constitutes a linearly independent and dense set on the boundary with respect to the L-2-norm. Tikhonov regularization in combination with the L-curve rule is incorporated to generate a stable solution to the obtained systems of linear equations. The proposed MFS approximation for the time-dependent lateral Cauchy problem is supported by numerical results.
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7.
  • Chapko, R., et al. (författare)
  • Calculating Heat and Wave Propagation from the Lateral Cauchy Data
  • 2022
  • Ingår i: Ukrainian Mathematical Journal. - : SPRINGER. - 0041-5995 .- 1573-9376. ; 74, s. 314-326
  • Tidskriftsartikel (refereegranskat)abstract
    • We present an overview of recent methods based on semidiscretization (in time) for the inverse ill-posed problems of finding the solutions of evolution equations according to the time-like Cauchy data. Specifically, the values of function and normal derivative are given on a portion of the lateral boundary of a space-time cylinder and the corresponding data should be generated on the remaining lateral part of the cylinder either for the heat equation or for the wave equation. The procedure of semidiscretization in time is based on the application either of the Laguerre transform or of the Rothe method (finite-difference approximation), and has a specific feature that similar sequences of elliptic problems are obtained for the heat and wave equations, and only the values of some parameters are different. The elliptic equations are solved numerically either by the boundary integral approach involving the Nystrom method or by the method of fundamental solutions. The theoretical properties are formulated together with discretization strategies in the space. Systems of linear equations are obtained for finding either the values of densities or the coefficients. The Tikhonov regularization is applied for the stable solution of the linear equations. The presented numerical results show that the proposed strategies give good accuracy in combination with economic computational costs.
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8.
  • Johansson, Tomas, 1976- (författare)
  • En omskrivning av cosinussatsen med historik
  • 2022
  • Rapport (övrigt vetenskapligt/konstnärligt)abstract
    • En omskrivning av cosinussatsen presenteras. Från arbeten av Stjernhjelm och Pitiscus visas att omskrivningen kan tolkas som en tillämpning av sekantsatsen. Vidare erhålls en formel för att beräkna längderna av de två segment som bildas då en sida i en triangel delas av en höjd, givet triangelns sidor. En sådan explicit formel går tillbaka till Ptolemaios. Hänvisningar med historik kring cosinussatsen och trigonometriska tabeller ges också.A summary in English is given at the end on page 10.
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9.
  • Johansson, Tomas, 1976- (författare)
  • Unwrapping a conic section
  • 2022
  • Rapport (övrigt vetenskapligt/konstnärligt)abstract
    • To enhance understanding when analysing the intersection between a cone and a plane, it is helpful to have a simple 3-dimensional paper model of the intersection. In this note, it is shown how the conic sections appear when the cone is unwrapped (flattened). Equations for the flattened conic intersections together with a printable figure and some LaTeX code for experiments are included
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10.
  • Arkitektur & teknik 2020/21, Årskurs 3, et al. (författare)
  • Resedagbok Schweiz augusti 2021
  • 2021
  • Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
    • Arkitektur och tekniks årliga studieresa till Schweiz är på många sätt unik. Vi transporterar oss själva genom det vackra alplandskapet och besöker några av landets vackraste broar och byggnader. De vilda bergsmassiven och den förfinade byggnadskulturen väver sig in i varandra under hela vår magiska arkitektursafari. Resan i augusti 2021 blev nästan ett år försenad på grund av pandemin. I stället för en förberedelse av studierna i årskurs 3 blev det en festlig avslutning på kandidattiden på Chalmers. Vid sidan om våra gängse besöksmål, från Robert Maillarts och Jürg Conzetts konstruktioner till Le Corbusier och Peter Zumthors arkitektur, hade vi den här resan ett särskilt fokus på materialen lera, kalk, sten och cement, och på restaurering av broar och byggnader i dessa material.
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