5 papers
Stable factorization of the Calderón problem via the Born approximation
Thierry Daudé, Fabricio MaciÃ, Cristóbal Meroño +1
In this article, we prove the existence of the Born approximation in the context of the radial Calderón problem for Schrödinger operators. The Born approximation naturally appear…
Mathematical analysis of one-layer neural network with fixed biases, a new activation function and other observations
Fabricio MaciÃ, Shu Nakamura
We analyze a simple one-hidden-layer neural network with ReLU activation functions and fixed biases, with one-dimensional input and output. We study both continuous and discrete ve…
Characterization of Dirichlet-to-Neumann maps via the Born approximation
Carlos Castro, Fabricio MaciÃ, Cristóbal Meroño +1
The problem of identifying the set of Dirichlet-to-Neumann (DtN) maps arising from conductivities on a smooth domain, among operators acting on functions on the boundary, is a chal…
The spectrum of Dirichlet-to-Neumann maps for radial conductivities
Thierry Daudé, Fabricio MaciÃ, Cristóbal Meroño +1
The problem of characterizing sequences of real numbers that arise as spectra of Dirichlet-to-Neumann (DtN) maps for elliptic operators has attracted considerable attention over th…
The Born approximation for the fixed energy Calderón problem
Fabricio MaciÃ, Cristóbal Meroño, Daniel Sánchez-Mendoza
The Born approximation of a potential in the context of the Calderón inverse problem is an object that can be formally defined in terms of spectral data of the Dirichlet-to-Neuman…