| 1. |
- Gad, Helge, et al.
(author)
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MTH1 inhibition eradicates cancer by preventing sanitation of the dNTP pool
- 2014
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In: Nature. - : Nature Publishing Group. - 0028-0836 .- 1476-4687. ; 508:7495, s. 215-221
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Journal article (peer-reviewed)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.
(author)
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Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations
- 2021
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In: Bulletin of the Iranian Mathematical Society. - : Springer. - 1735-8515 .- 1017-060X. ; 47, s. 1681-1699
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Journal article (peer-reviewed)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-
(author)
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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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Licentiate thesis (other academic/artistic)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-
(author)
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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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Doctoral thesis (other academic/artistic)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, et al.
(author)
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Reconstruction of the Radiation Condition and Solution for the Helmholtz Equation in a Semi-infinite Strip from Cauchy Data on an Interior Segment
- 2023
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In: Computational Methods in Applied Mathematics. - : WALTER DE GRUYTER GMBH. - 1609-4840 .- 1609-9389.
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Journal article (peer-reviewed)abstract
- We consider an inverse problem for the Helmholtz equation of reconstructing a solution from measurements taken on a segment inside a semi-infinite strip. Homogeneous Neumann conditions are prescribed on both side boundaries of the strip and an unknown Dirichlet condition on the remaining part of the boundary. Additional complexity is that the radiation condition at infinity is unknown. Our aim is to find the unknown function in the Dirichlet boundary condition and the radiation condition. Such problems appear in acoustics to determine acoustical sources and surface vibrations from acoustic field measurements. The problem is split into two sub-problems, a well-posed and an ill-posed problem. We analyse the theoretical properties of both problems; in particular, we show that the radiation condition is described by a stable non-linear problem. The second problem is ill-posed, and we use the Landweber iteration method together with the discrepancy principle to regularize it. Numerical tests show that the approach works well.
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| 6. |
- Achieng, Pauline, 1990-, et al.
(author)
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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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In: Journal of Inverse and Ill-Posed Problems. - : WALTER DE GRUYTER GMBH. - 0928-0219 .- 1569-3945. ; 31:5
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Journal article (peer-reviewed)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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| 7. |
- Andersson, Viktor, 1983, et al.
(author)
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Efficient Utilization of Industrial Excess Heat for Post-combustion CO2 Capture: An Oil Refinery Sector Case Study
- 2014
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In: Energy Procedia. - : Elsevier BV. - 1876-6102. ; 63, s. 6548-6556
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Conference paper (peer-reviewed)abstract
- A key issue in post-combustion carbon capture is the choice of absorbent. In this paper two different absorbents, monoethanolamine (MEA) and ammonia (NH3), have been modeled in Aspen Plus at different temperatures for possible implementation at an oil refinery. The focus of investigation is the possibilities of heat integration between the oil refinery and the carbon capture process and how these possibilities could change in a future situation where energy efficiency measures have been implemented.The results show that if only using excess heat from the refinery for heating of the carbon capture process, the MEA process can capture more CO2 than the NH3 process. It is shown that the configuration requiring least supplementary heat when applying carbon capture to all flue gases is MEA at 120 °C.The temperature profile of the excess heat from the refinery suits the MEA and NH3 processes differently. The NH3 process would benefit from a flat section above 100 °C to better integrate the heat needed to reduce slip, while the MEA process only needs heat at stripper temperature.
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| 8. |
- Arop, Martin Deosborns, et al.
(author)
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Optimal Actuator Placement for Control of Vibrations Induced by Pedestrian-Bridge Interactions
- 2023
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In: MATHEMATICS IN APPLIED SCIENCES AND ENGINEERING. - : WESTERN LIBRARIES. - 2563-1926. ; 4:3, s. 172-195
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Journal article (peer-reviewed)abstract
- In this paper, an optimal actuator placement problem with a linear wave equation as the constraint is considered. In particular, this work presents the frameworks for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical results are consistent with the theoretical results, in the two examples considered.
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| 9. |
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| 10. |
- Berntsson, Fredrik, et al.
(author)
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A Data Assimilation Approach to Coefficient Identification
- 2011
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Reports (other academic/artistic)abstract
- The thermal conductivity properties of a material can be determined experimentally by using temperature measurements taken at specified locations inside the material. We examine a situation where the properties of a (previously known) material changed locally. Mathematically we aim to find the coefficient k(x) in the stationary heat equation (kTx)x = 0;under the assumption that the function k(x) can be parametrized using only a few degrees of freedom. The coefficient identification problem is solved using a least squares approach; where the (non-linear) control functional is weighted according to the distribution of the measurement locations. Though we only discuss the 1D case the ideas extend naturally to 2D or 3D. Experimentsdemonstrate that the proposed method works well.
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