| 1. |
- Zhang, Ye, 1984-, et al.
(författare)
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Reconstructing gas distribution maps via an adaptive sparse regularization algorithm
- 2016
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Ingår i: Inverse Problems in Science and Engineering. - : Taylor & Francis. - 1741-5977 .- 1741-5985. ; 24:7, s. 1186-1204
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.
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| 2. |
- Zhang, Ye, 1984-, et al.
(författare)
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An optimal regularization method for convolution equations on the sourcewise represented set
- 2015
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Ingår i: Journal of Inverse and Ill-Posed Problems. - Berlin, Germany : Walter de Gruyter. - 0928-0219 .- 1569-3945. ; 23:5, s. 465-475
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider an inverse problem for the integral equation of the convolution typein a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a prioriinformation (sourcewise representation) based on optimal recovery theory we propose a new method. Theregularization and optimization properties of this method are proved. An optimal minimal a priori error ofthe problem is found. Moreover, a so-called optimal regularized approximate solution and its correspondingerror estimation are considered. Eciency and applicability of this method are demonstrated in a numericalexample of the image deblurring problem with noisy data.
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| 3. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Mapping class group representations from Drinfeld doubles of finite groups
- 2020
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Ingår i: Journal of knot theory and its ramifications. - : World Scientific Publishing Co. Pte Ltd. - 0218-2165. ; 29:5
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Tidskriftsartikel (refereegranskat)abstract
- We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.
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| 4. |
- Gulliksson, Mårten, 1963-, et al.
(författare)
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An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection
- 2020
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Ingår i: Computational Economics. - : Springer. - 0927-7099 .- 1572-9974. ; 56, s. 773-794
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Tidskriftsartikel (refereegranskat)abstract
- Covariance matrix of the asset returns plays an important role in the portfolioselection. A number of papers is focused on the case when the covariance matrixis positive definite. In this paper, we consider portfolio selection with a singu-lar covariance matrix. We describe an iterative method based on a second orderdamped dynamical systems that solves the linear rank-deficient problem approxi-mately. Since the solution is not unique, we suggest one numerical solution that canbe chosen from the iterates that balances the size of portfolio and the risk. The nu-merical study confirms that the method has good convergence properties and givesa solution as good as or better than the constrained least norm Moore-Penrose solu-tion. Finally, we complement our result with an empirical study where we analyzea portfolio with actual returns listed in S&P 500 index.
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| 5. |
- Andersen, Jørgen Ellegaard, et al.
(författare)
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Reducibility of quantum representations of mapping class groups
- 2010
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Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 91:3, s. 215-239
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.
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| 6. |
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| 7. |
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| 8. |
- Bergwall, Andreas, 1972-
(författare)
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Conceptualizing reasoning-and-proving opportunities in textbook expositions : Cases from secondary calculus
- 2017
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Ingår i: Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017). - Dublin, Ireland : European Society for Research in Mathematics Education. - 9781873769737 ; , s. 91-98
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Konferensbidrag (refereegranskat)abstract
- Several recent textbook studies focus on opportunities to learn reasoning-and-proving. They typically investigate the extent to which justifications are general proofs and what opportunities exist for learning important elements of mathematical reasoning. In this paper, I discuss how a particular analytical framework for this might be refined. Based on an in-depth analysis of certain textbook passages in upper secondary calculus textbooks, I make an account for analytical issues encountered during this process and identify aspects of reasoning-and-proving in textbooks that might be missed unless the framework is refined. Among them there are characterizations of generality, use of different representations, logical and mathematical structure, and ordering of material and student activities. Finally, implications beyond textbook research are discussed.
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| 9. |
- Bergwall, Andreas, 1972-
(författare)
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On a generality framework for proving tasks
- 2015
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Ingår i: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - Prague : Charles University in Prague, Faculty of Education and ERME. - 9788072908448 ; , s. 86-92
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Konferensbidrag (refereegranskat)abstract
- In this paper I present an analytic framework for generality in textbook proving tasks that involve functions. The framework is discussed in relation to results obtained when analysing tasks in integral calculus. The results show that the frameworks’ categories are easily distinguishable if the functions are explicitly described. The results are also promising regarding the possibility to clarify differences between textbooks. The analysed sections exemplify that there is not necessarily a correlation between the number of general proving tasks and the opportunities for students to engage in reasoning about arbitrary functions. Limitations and possible refinements of the framework are also discussed.
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| 10. |
- Bergwall, Andreas, 1972-, et al.
(författare)
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The State of Proof in Finnish and Swedish Mathematics Textbooks : Capturing Differences in Approaches to Upper-Secondary Integral Calculus
- 2017
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Ingår i: Mathematical Thinking and Learning. - : Taylor & Francis. - 1098-6065 .- 1532-7833. ; 19:1, s. 1-18
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Tidskriftsartikel (refereegranskat)abstract
- Students’ difficulties with proof, scholars’ calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related reasoning in integral calculus, a key subject in transitioning from secondary to tertiary education. We analyze expository sections and nearly 2000 students’ exercises in the four most frequently used Finnish and Swedish textbook series. Results indicate that Finnish textbooks offer more opportunities for learning proof than do Swedish textbooks. Proofs are also more visible in Finnish text-books than in Swedish materials, but the tasks in the latter reflect a higher variation in nature of proof-related reasoning. Our results are compared with methodologically similar U.S. studies. Consequences for learning and transition to university mathematics, as well as directions for future research, are discussed.
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