Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Nielsen, Bjorn Fredrik"'
We propose and analyze a procedure for using a standard activity-based neuron network model and firing data to compute the effective connection strengths between neurons in a network. We assume a Heaviside response function, that the external inputs
Externí odkaz:
http://arxiv.org/abs/2409.07241
For linear ill-posed problems with nontrivial null spaces, Tikhonov regularization and truncated singular value decomposition (TSVD) typically yield solutions that are close to the minimum norm solution. Such a bias is not always desirable, and we ha
Externí odkaz:
http://arxiv.org/abs/2408.17074
We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard results for subgradients, we derive simple-to-check criteria which assu
Externí odkaz:
http://arxiv.org/abs/2212.04187
We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box constraints, combined with weighted sparsity regularization, can enable
Externí odkaz:
http://arxiv.org/abs/2206.06069
This paper deals with the generalized spectrum of continuously invertible linear operators defined on infinite dimensional Hilbert spaces. More precisely, we consider two bounded, coercive, and self-adjoint operators $\bc{A, B}: V\mapsto V^{\#}$, whe
Externí odkaz:
http://arxiv.org/abs/2103.00849
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results for these a
Externí odkaz:
http://arxiv.org/abs/2012.11280
We study whether a modified version of Tikhonov regularization can be used to identify several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This paper extends the results presented in [5]. It turns out that the possibil
Externí odkaz:
http://arxiv.org/abs/2011.04394
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significant nullspace. Standard Tikhonov regularization yields solutions which a
Externí odkaz:
http://arxiv.org/abs/2005.09444
We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral decomposition $K=Q
Externí odkaz:
http://arxiv.org/abs/2002.00676
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