| 1. |
- Gad, Helge, et al.
(författare)
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MTH1 inhibition eradicates cancer by preventing sanitation of the dNTP pool
- 2014
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Ingår i: Nature. - : Nature Publishing Group. - 0028-0836 .- 1476-4687. ; 508:7495, s. 215-221
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Tidskriftsartikel (refereegranskat)abstract
- Cancers have dysfunctional redox regulation resulting in reactive oxygen species production, damaging both DNA and free dNTPs. The MTH1 protein sanitizes oxidized dNTP pools to prevent incorporation of damaged bases during DNA replication. Although MTH1 is non-essential in normal cells, we show that cancer cells require MTH1 activity to avoid incorporation of oxidized dNTPs, resulting in DNA damage and cell death. We validate MTH1 as an anticancer target in vivo and describe small molecules TH287 and TH588 as first-in-class nudix hydrolase family inhibitors that potently and selectively engage and inhibit the MTH1 protein in cells. Protein co-crystal structures demonstrate that the inhibitors bindin the active site of MTH1. The inhibitors cause incorporation of oxidized dNTPs in cancer cells, leading to DNA damage, cytotoxicity and therapeutic responses in patient-derived mouse xenografts. This study exemplifies the non-oncogene addiction concept for anticancer treatment and validates MTH1 as being cancer phenotypic lethal.
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| 2. |
- Achieng, Pauline, 1990-, et al.
(författare)
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Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
- 2021
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Ingår i: Bulletin of the Iranian Mathematical Society. - : Springer. - 1735-8515 .- 1017-060X. ; 47, s. 1681-1699
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Tidskriftsartikel (refereegranskat)abstract
- The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers k2, in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of k2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.
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| 3. |
- Achieng, Pauline, 1990-
(författare)
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Analysis of the Robin-Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study the Cauchy problem for elliptic equations. It arises in many areas of application in science and engineering as a problem of reconstruction of solutions to elliptic equations in a domain from boundary measurements taken on a part of the boundary of this domain. The Cauchy problem for elliptic equations is known to be ill-posed.We use an iterative regularization method based on alternatively solving a sequence of well-posed mixed boundary value problems for the same elliptic equation. This method, based on iterations between Dirichlet-Neumann and Neumann-Dirichlet mixed boundary value problems was first proposed by Kozlov and Maz’ya [13] for Laplace equation and Lame’ system but not Helmholtz-type equations. As a result different modifications of this original regularization method have been proposed in literature. We consider the Robin-Dirichlet iterative method proposed by Mpinganzima et.al [3] for the Cauchy problem for the Helmholtz equation in bounded domains.We demonstrate that the Robin-Dirichlet iterative procedure is convergent for second order elliptic equations with variable coefficients provided the parameter in the Robin condition is appropriately chosen. We further investigate the convergence of the Robin-Dirichlet iterative procedure for the Cauchy problem for the Helmholtz equation in a an unbounded domain. We derive and analyse the necessary conditions needed for the convergence of the procedure.In the numerical experiments, the precise behaviour of the procedure for different values of k2 in the Helmholtz equation is investigated and the results show that the speed of convergence depends on the choice of the Robin parameters, μ0 and μ1. In the unbounded domain case, the numerical experiments demonstrate that the procedure is convergent provided that the domain is truncated appropriately and the Robin parameters, μ0 and μ1 are also chosen appropriately.
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| 4. |
- Achieng, Pauline, 1990-
(författare)
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Reconstruction of solutions of Cauchy problems for elliptic equations in bounded and unbounded domains using iterative regularization methods
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Cauchy problems for elliptic equations arise in applications in science and engineering. These problems often involve finding important information about an elliptical system from indirect or incomplete measurements. Cauchy problems for elliptic equations are known to be disadvantaged in the sense that a small pertubation in the input can result in a large error in the output. Regularization methods are usually required in order to be able to find stable solutions. In this thesis we study the Cauchy problem for elliptic equations in both bounded and unbounded domains using iterative regularization methods. In Paper I and II, we focus on an iterative regularization technique which involves solving a sequence of mixed boundary value well-posed problems for the same elliptic equation. The original version of the alternating iterative technique is based on iterations alternating between Dirichlet-Neumann and Neumann-Dirichlet boundary value problems. This iterative method is known to possibly work for Helmholtz equation. Instead we study a modified version based on alternating between Dirichlet-Robin and Robin-Dirichlet boundary value problems. First, we study the Cauchy problem for general elliptic equations of second order with variable coefficients in a limited domain. Then we extend to the case of unbounded domains for the Cauchy problem for Helmholtz equation. For the Cauchy problem, in the case of general elliptic equations, we show that the iterative method, based on Dirichlet-Robin, is convergent provided that parameters in the Robin condition are chosen appropriately. In the case of an unbounded domain, we derive necessary, and sufficient, conditions for convergence of the Robin-Dirichlet iterations based on an analysis of the spectrum of the Laplacian operator, with boundary conditions of Dirichlet and Robin types.In the numerical tests, we investigate the precise behaviour of the Dirichlet-Robin iterations, for different values of the wave number in the Helmholtz equation, and the results show that the convergence rate depends on the choice of the Robin parameter in the Robin condition. In the case of unbounded domain, the numerical experiments show that an appropriate truncation of the domain and an appropriate choice of Robin parameter in the Robin condition lead to convergence of the Robin-Dirichlet iterations.In the presence of noise, additional regularization techniques have to implemented for the alternating iterative procedure to converge. Therefore, in Paper III and IV we focus on iterative regularization methods for solving the Cauchy problem for the Helmholtz equation in a semi-infinite strip, assuming that the data contains measurement noise. In addition, we also reconstruct a radiation condition at infinity from the given Cauchy data. For the reconstruction of the radiation condition, we solve a well-posed problem for the Helmholtz equation in a semi-infinite strip. The remaining solution is obtained by solving an ill-posed problem. In Paper III, we consider the ordinary Helmholtz equation and use seperation of variables to analyze the problem. We show that the radiation condition is described by a non-linear well-posed problem that provides a stable oscillatory solution to the Cauchy problem. Furthermore, we show that the ill–posed problem can be regularized using the Landweber’s iterative method and the discrepancy principle. Numerical tests shows that the approach works well.Paper IV is an extension of the theory from Paper III to the case of variable coefficients. Theoretical analysis of this Cauchy problem shows that, with suitable bounds on the coefficients, can iterative regularization methods be used to stabilize the ill-posed Cauchy problem.
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| 5. |
- Achieng, Pauline, 1990-, et al.
(författare)
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Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain
- 2023
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Ingår i: Journal of Inverse and Ill-Posed Problems. - : WALTER DE GRUYTER GMBH. - 0928-0219 .- 1569-3945. ; 31:5
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Tidskriftsartikel (refereegranskat)abstract
- We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.
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| 6. |
- Berntsson, Fredrik, 1971-, et al.
(författare)
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A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients
- 2018
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- One dimensional models for fluid flow in tubes are frequently used tomodel complex systems, such as the arterial tree where a large numberof vessels are linked together at bifurcations. At the junctions transmission conditions are needed. One popular option is the classic Kirchhoffconditions which means conservation of mass at the bifurcation andprescribes a continuous pressure at the joint.In reality the boundary layer phenomena predicts fast local changesto both velocity and pressure inside the bifurcation. Thus it is not appropriate for a one dimensional model to assume a continuous pressure. In this work we present a modification to the classic Kirchhoff condi-tions, with a symmetric pressure drop matrix, that is more suitable forone dimensional flow models. An asymptotic analysis, that has beencarried out previously shows that the new transmission conditions hasen exponentially small error.The modified transmission conditions take the geometry of the bifurcation into account and can treat two outlets differently. The conditions can also be written in a form that is suitable for implementationin a finite difference solver. Also, by appropriate choice of the pressuredrop matrix we show that the new transmission conditions can producehead loss coefficients similar to experimentally obtained ones.
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| 7. |
- Berntsson, Fredrik, 1971-, et al.
(författare)
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A one-dimensional model of a false aneurysm
- 2017
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Ingår i: International Journal of Research in Engineering and Science (IJRES). - : IJRES. - 2320-9356 .- 2320-9364. ; 5:6, s. 61-73
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Tidskriftsartikel (refereegranskat)abstract
- A false aneurysm is a hematoma, i.e. collection ofblood outside of a blood vessel, that forms due to a hole in the wall of an artery . This represents a serious medical condition that needs to be monitored and, under certain conditions, treatedurgently. In this work a one-dimensional model of a false aneurysm isproposed. The new model is based on a one-dimensional model of anartery previously presented by the authors and it takes into accountthe interaction between the hematoma and the surrounding musclematerial. The model equations are derived using rigorous asymptoticanalysis for the case of a simplified geometry. Even though the model is simple it still supports a realisticbehavior for the system consisting of the vessel and the hematoma. Using numerical simulations we illustrate the behavior ofthe model. We also investigate the effect of changing the size of the hematoma. The simulations show that ourmodel can reproduce realistic solutions. For instance we show thetypical strong pulsation of an aneurysm by blood entering the hematoma during the work phase of the cardiac cycle, and the blood returning tothe vessel during the resting phase. Also we show that the aneurysmgrows if the pulse rate is increased due to, e.g., a higher work load.
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| 8. |
- Berntsson, Fredrik, 1971-, et al.
(författare)
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More on Estimation of Banded and Banded Toeplitz Covariance Matrices
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we consider two different linear covariance structures, e.g., banded and bended Toeplitz, and how to estimate them using different methods, e.g., by minimizing different norms.One way to estimate the parameters in a linear covariance structure is to use tapering, which has been shown to be the solution to a universal least squares problem. We know that tapering not always guarantee the positive definite constraints on the estimated covariance matrix and may not be a suitable method. We propose some new methods which preserves the positive definiteness and still give the correct structure.More specific we consider the problem of estimating parameters of a multivariate normal p–dimensional random vector for (i) a banded covariance structure reflecting m–dependence, and (ii) a banded Toeplitz covariance structure.
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| 9. |
- Berntsson, Fredrik, 1971-
(författare)
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Numerical methods for inverse heat conduction problems
- 2001
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In many industrial applications one wishes to determine the temperature history on the surface of a body, where the surface itself is inaccessible for measurements. The sideways heat equation is a model of this situation. In a one-dimensional setting this is formulated mathematically as a Cauchy problem for the heat equation, where temperature and heat--flux data are available along the line x=1, and a solution is sought for 0 ≤ x< 1. This problem is ill-posed in the sense that the solution does not depend continuously on the data. Stability can be restored by replacing the time derivative in the heat equation by a bounded approximation. We consider both spectral and wavelet approximations of the derivative. The resulting problem is a system of ordinary differential equations in the space variable, that can be solved using standard methods, e.g. a Runge-Kutta method. The methods are analyzed theoretically, and error estimates are derived, that can be used for selecting the appropriate level of regularization. The numerical implementation of the proposed methods is discussed. Numerical experiments demonstrate that the proposed methods work well, and can be implemented efficiently. Furthermore, the numerical methods can easily be adapted to solve problems with variable coefficients, and also non-linear equations. As test problems we take model equations, with constant and variable coefficients. Also, we solve problems from applications, with actual measured data.Inverse problems for the stationary heat equation are also discussed. Suppose that the Laplace equation is valid in a domain with a hole. Temperature and heat-flux data are given on the outer boundary, and we wish to compute the steady state temperature on the inner boundary. A standard approach is to discretize the equation by finite differences, and use Tikhonov's method for stabilizing the discrete problem, which leads to a large sparse least squares problem. Alternatively, we propose to use a conformal mapping to transform the domain into an annulus, where the equivalent problem can be solved using separation of variables. The ill-posedness is dealt with by filtering away high frequencies from the solution. Numerical results using both methods are presented. A closely related problem is that of determining the stationary temperature inside a body, from temperature and heat-flux measurements on a part of the boundary. In practical applications it is sometimes the case that the domain, where the differential equation is valid, is partly unknown. In such cases we want to determine not only the temperature, but also the shape of the boundary of the domain. This problem arises, for instance, in iron production, where the walls of a melting furnace is subject to both physical and chemical wear. In order to avoid a situation where molten metal breaks out through the walls the thickness of the walls should be constantly monitored. This is done by solving an inverse problem for the stationary heat equation, where temperature and heat-flux data are available at certain locations inside the walls of the furnace. Numerical results are presented also for this problem.
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| 10. |
- Berntsson, Fredrik, 1971-, et al.
(författare)
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Numerical Solution of Cauchy Problems for Elliptic Equations in "Rectangle-like" Geometries
- 2005
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Ingår i: FEMLAB Conference,2005. - Stockholm : Comsol AB.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We consider two dimensional inverse steady state heat conduction problems in complex geometries. The coefficients of the elliptic equation are assumed to be non-constant. Cauchy data are given on one part of the boundary and we want to find the solution in the whole domain. The problem is ill--posed in the sense that the solution does not depend continuously on the data. Using an orthogonal coordinate transformation the domain is mapped onto a rectangle. The Cauchy problem can then be solved by replacing one derivative by a bounded approximation. The resulting well--posed problem can then be solved by a method of lines. A bounded approximation of the derivative can be obtained by differentiating a cubic spline, that approximate the function in the least squares sense. This particular approximation of the derivative is computationally efficient and flexible in the sense that its easy to handle different kinds of boundary conditions. This inverse problem arises in iron production, where the walls of a melting furnace are subject to physical and chemical wear. Temperature and heat--flux data are collected by several thermocouples located inside the walls. The shape of the interface between the molten iron and the walls can then be determined by solving an inverse heat conduction problem. In our work we make extensive use of Femlab for creating test problems. By using Femlab we solve relatively complex model problems for the purpose of creating numerical test data used for validating our methods. For the types of problems we are intressted in numerical artefacts appear, near corners in the domain, in the gradients that Femlab calculates. We demonstrate why this happen and also how we deal with the problem.
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