| 1. |
- Belmeguenai, Amor, et al.
(författare)
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Intrinsic Plasticity Complements Long-Term Potentiation in Parallel Fiber Input Gain Control in Cerebellar Purkinje Cells
- 2010
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Ingår i: The Journal of Neuroscience. - 1529-2401. ; 30:41, s. 13630-13643
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Tidskriftsartikel (refereegranskat)abstract
- Synaptic gain control and information storage in neural networks are mediated by alterations in synaptic transmission, such as in long-term potentiation (LTP). Here, we show using both in vitro and in vivo recordings from the rat cerebellum that tetanization protocols for the induction of LTP at parallel fiber (PF)-to-Purkinje cell synapses can also evoke increases in intrinsic excitability. This form of intrinsic plasticity shares with LTP a requirement for the activation of protein phosphatases 1, 2A, and 2B for induction. Purkinje cell intrinsic plasticity resembles CA1 hippocampal pyramidal cell intrinsic plasticity in that it requires activity of protein kinaseA (PKA) and case in kinase 2 (CK2) and is mediated by a downregulation of SK-type calcium-sensitive K conductances. In addition, Purkinje cell intrinsic plasticity similarly results in enhanced spine calcium signaling. However, there are fundamental differences: first, while in the hippocampus increases in excitability result in a higher probability for LTP induction, intrinsic plasticity in Purkinje cells lowers the probability for subsequent LTP induction. Second, intrinsic plasticity raises the spontaneous spike frequency of Purkinje cells. The latter effect does not impair tonic spike firing in the target neurons of inhibitory Purkinje cell projections in the deep cerebellar nuclei, but lowers the Purkinje cell signal-to-noise ratio, thus reducing the PF readout. These observations suggest that intrinsic plasticity accompanies LTP of active PF synapses, while it reduces at weaker, nonpotentiated synapses the probability for subsequent potentiation and lowers the impact on the Purkinje cell output.
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| 2. |
- de Jeu, Marcel, et al.
(författare)
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Algebraic curves for commuting elements in the $q$-deformed Heisenberg algebra
- 2009
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 321:4, s. 1239-1255
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.
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| 3. |
- de Jeu, Marcel, et al.
(författare)
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On the Banach *-algebra crossed product associated with a topological dynamical system
- 2012
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 262:11, s. 4746-4765
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Tidskriftsartikel (refereegranskat)abstract
- Given a topological dynamical system Sigma = (X, sigma), where X is a compact Hausdorff space and a a homeomorphism of X, we introduce the Banach *-algebra crossed product l(1) (E) most naturally associated with Sigma and initiate its study. It has a richer structure than its well investigated C*-envelope, as becomes evident from the possible existence of non-self-adjoint closed ideals. We link its ideal structure to the dynamics, determining when the algebra is simple, or prime, and when there exists a non-self-adjoint closed ideal. A structure theorem is obtained when X consists of one finite orbit, and the algebra is shown to be Hermitian if X is finite. The key lies in analysing the commutant of C(X) in the algebra, which is shown to be a maximal abelian subalgebra with non-zero intersection with each non-zero closed ideal. (C) 2012 Elsevier Inc. All rights reserved.
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| 4. |
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| 5. |
- Silvestrov, Sergei, 1970-, et al.
(författare)
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Algebraic dependence of commuting elements in algebras
- 2009
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Ingår i: Generalized Lie theory in mathematics, physics and beyond. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540853312 - 9783540853329 ; , s. 265-280
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Bokkapitel (refereegranskat)abstract
- The aim of this paper to draw attention to several aspects of the algebraic dependence in algebras. The article starts with discussions of the algebraic dependence problem in commutative algebras. Then the Burchnall—Chaundy construction for proving algebraic dependence and obtaining the corresponding algebraic curves for commuting differential operators in the Heisenberg algebra is reviewed. Next some old and new results on algebraic dependence of commuting q-difference operators and elements in q-deformed Heisenberg algebras are reviewed. The main ideas and essence of two proofs of this are reviewed and compared. One is the algorithmic dimension growth existence proof. The other is the recent proof extending the Burchnall–Chaundy approach from differential operators and the Heisenberg algebra to the q-deformed Heisenberg algebra, showing that the Burchnall—Chaundy eliminant construction indeed provides annihilating curves for commuting elements in the q-deformed Heisenberg algebras for q not a root of unity.
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| 6. |
- Silvestrov, Sergei, et al.
(författare)
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Dynamical systems and commutants in crossed products
- 2007
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 18:4, s. 455-471
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers.
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| 7. |
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| 8. |
- Svensson, Christian, et al.
(författare)
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Dynamical systems associated with crossed products
- 2009
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 547-559
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system.
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