| 1. |
- Lavau, S., et al.
(författare)
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Infinity-enhancing of Leibniz algebras
- 2020
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Ingår i: Letters in Mathematical Physics. - : Springer Science and Business Media LLC. - 0377-9017 .- 1573-0530. ; 110, s. 3121-52
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Tidskriftsartikel (refereegranskat)abstract
- We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies (Bonezzi and Hohm in Commun Math Phys 377:2027-2077, 2020), and differential graded Lie algebras, which have been already used in this context. We explain how any Leibniz algebra gives rise to a differential graded Lie algebra with a corresponding infinity-enhanced Leibniz algebra. Moreover, by a theorem of Getzler, this differential graded Lie algebra canonically induces an L-infinity-algebra structure on the suspension of the underlying chain complex. We explicitly give the brackets to all orders and show that they agree with the partial results obtained from the infinity-enhanced Leibniz algebras in Bonezzi and Hohm (Commun Math Phys 377:2027-2077, 2020).
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| 2. |
- Dmytryshyn, Andrii, 1986-, et al.
(författare)
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Miniversal deformations of matrices of bilinear forms
- 2012
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 436:7, s. 2670-2700
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Tidskriftsartikel (refereegranskat)abstract
- Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29–43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence.
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| 3. |
- Bossard, Guillaume, et al.
(författare)
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Generalised diffeomorphisms for E9
- 2017
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Ingår i: Physical Review D - Particles, Fields, Gravitation and Cosmology. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 96, s. 106022-
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Tidskriftsartikel (refereegranskat)abstract
- We construct generalised diffeomorphisms for E9 exceptional field theory. The trans- formations, which like in the E8 case contain constrained local transformations, close when acting on fields. This is the first example of a generalised diffeomorphism alge- bra based on an infinite-dimensional Lie algebra and an infinite-dimensional coordi- nate module. As a byproduct, we give a simple generic expression for the invariant tensors used in any extended geometry. We perform a generalised Scherk–Schwarz reduction and verify that our transformations reproduce the structure of gauged supergravity in two dimensions. The results are valid also for other affine algebras.
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| 4. |
- Eriksen, Niklas, 1974-
(författare)
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Approximating the expected number of inversions given the number of breakpoints
- 2002
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Ingår i: Lecture Notes in Computer Science. - Berlin, Germany : Springer Berlin/Heidelberg. - 0302-9743 .- 1611-3349. - 3540442111 ; 2452, s. 316-330
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Tidskriftsartikel (refereegranskat)abstract
- We look at a problem with motivation from computational biology: Given the number of breakpoints in a permutation (representing a gene sequence), compute the expected number of inversions that have occured. For this problem, we obtain an analytic approximation that is correct within a percent or two. For the inverse problem, computing the expected number of breakpoints after any number of inversions, we obtain an analytic approximation with an error of less than a hundredth of a breakpoint.
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| 5. |
- Eriksen, Niklas, 1974-
(författare)
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Expected number of breakpoints after t random reversals in genomes with duplicate genes
- 2008
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Ingår i: Discrete Applied Mathematics. - Amsterdam, Netherlands : Elsevier. - 0166-218X .- 1872-6771. ; 156:12, s. 2320-2335
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Tidskriftsartikel (refereegranskat)abstract
- In comparative genomics, one wishes to deduce the evolutionary distance between different species by studying their genomes. Using gene order information, we seek the number of times the gene order has changed between two species. One approach is to compute the method of moments estimate of this edit distance from a measure of dissimilarity called the breakpoint measure. In this paper, we extend formulae and bounds of this estimate on gene permutations to genomes with duplicate genes.
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| 6. |
- Eriksen, Niklas, 1974
(författare)
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Reversal and Transposition Medians
- 2007
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Ingår i: Theoretical Computer Science. - Amsterdam, Netherlands : Elsevier. ; 374:1-3, s. 111-126
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Tidskriftsartikel (refereegranskat)abstract
- In determining phylogenetic trees using gene order information, medians provide a powerful alternative to pairwise distances. On the other hand, both breakpoint and reversal medians are NP-hard to compute and the use of medians has been limited to relatively closely related genomes. In this paper, we show that in spite of the greater non-uniqueness of reversal medians, compared to breakpoint medians, medians of moderately distant genomes are often widely spread. This means that regardless of which approximation algorithms one may devise for computing reversal medians, the genomes need to be closely related for phylogenetic tree computations to be successful. To show this, we use results on transposition medians, which behave similarly, and also support our claims with simulations and a real data example with widely spread medians.
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| 7. |
- Eriksen, Niklas, 1974
(författare)
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The freshman's approach to Conway's napkin problem
- 2008
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Ingår i: The American mathematical monthly. - Washington, USA : Mathematical Association of America. - 0002-9890 .- 1930-0972. ; 115:6, s. 492-498
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Tidskriftsartikel (refereegranskat)abstract
- In the March 2006 issue of the MONTHLY, Claesson and Petersen gave a thorough solution to Conway's napkin problem. The problem is the following: Assume that n mathematicians arrive in random order at a conference dinner with a circular table, and that the napkins are placed exactly halfway between the plates so that the guests do not know whether they are supposed to use the right or the left napkin. Each guest prefers these napkins with probabilities p and 1-p, respectively, and tries her preferred alternative before trying the other, if the preferred napkin has been taken. Which proportion of guests is expected to sit down at a place where both adjacent napkins have been taken and thus be without a napkin? Claesson and Petersen use a system of generating functions to compute both the expectation and the variance of this proportion and to address similar questions, for instance regarding the number of guests who get a napkin though not the preferred one. However, these expectations can also be computed using purely elementary methods, such as the binomial theorem. We present the freshman's approach to the napkin problem and related problems, for instance the one with French diners mentioned, but not solved, by Claesson and Petersen.
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| 8. |
- Aksteiner, S., et al.
(författare)
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New identities for linearized gravity on the Kerr spacetime
- 2019
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Ingår i: Physical Review D. - : American Physical Society. - 2470-0010 .- 2470-0029. ; 99:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive a differential identity for linearized gravity on the Kerr spacetime and more generally on vacuum spacetimes of Petrov type D. We show that a linear combination of second derivatives of the linearized Weyl tensor can be formed into a complex symmetric 2-tensor M-ab which solves the linearized Einstein equations. The identity makes this manifest by relating M-ab to two terms solving the linearized Einstein equations by construction. The self-dual Weyl curvature of M-ab gives a covariant version of the Teukolsky-Starobinsky identities for linearized gravity which, in addition to the two classical identities for linearized Weyl scalars with extreme spin weights, includes three additional equations. In particular, they are not consequences of the classical Teukolsky-Starobinsky identities, but are additional integrability conditions for linearized gravity. The result has direct application in the construction of symmetry operators and also yields a set of nontrivial gauge invariants for linearized gravity.
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| 9. |
- 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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| 10. |
- Carbone, Lisa, et al.
(författare)
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Generators and relations for (generalised) Cartan type superalgebras
- 2019
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Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6588 .- 1742-6596. ; 1194:1
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Konferensbidrag (refereegranskat)abstract
- In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, A(n-1,0) = s (1|n) can be constructed by adding a "gray" node to the Dynkin diagram of An-1 = s (n), corresponding to an odd null root. The Cartan superalgebras constitute a difierent class, where the simplest example is Wpnq, the derivation algebra of the Grassmann algebra on n generators. Here we present a novel construction of Wpnq, from the same Dynkin diagram as A(n-1,0), but with additional generators and relations.
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