arXiv subjects

Sonia Foschiatti

Publications and source records attributed to Sonia Foschiatti.

7 recordsLinked to original sources

arXiv2026

ArcheoLab: A hands-on course to engage students in applied mathematics

In this paper, we describe ``Archeolab: Computed Tomography and Virtual Unwrapping of Scrolls'', an interdisciplinary undergraduate course guiding students through the virtual reading of scrolls. By studying the theoretical foundations of X-ray Computed Tomography, genetic algorithms, and conducting hands-on experiments and programming sessions, we aim to encourage students to study applied mathematics and promote active participation in lectures.

math.HO↗

arXiv2026

Identification of an inclusion from local Cauchy data for time-harmonic elastic waves

We consider the inverse problem of determining an inclusion contained in an elastic body undergoing time-harmonic oscillations at fixed frequency by local Cauchy data. Both the body and the inclusion are made by different homogeneous linearly elastic isotropic materials, with piecewise constant mass densities. Under mild a priori regularity assumptions on the unknown inclusion and with no spectral hypothesis on the frequency, we establish a logarithmic-type stability estimate by local Cauchy data. We also provide a stability result in terms of the so local Dirichlet to Neumann map for sufficiently small frequency.

math.AP↗

arXiv2025

Deciphering scrolls with tomography: A training experiment

The recovery of severely damaged ancient written documents has proven to be a major challenge for many scientists, mainly due to the impracticality of physical unwrapping them. Non-destructive techniques, such as X-ray computed tomography (CT), combined with computer vision algorithms, have emerged as a means of facilitating the virtual reading of the hidden contents of the damaged documents. This paper proposes an educational laboratory aimed at simulating the entire process of acquisition and virtual recovery of the ancient works. We have developed an experimental setup that uses visible light to replace the detrimental X-rays, and a didactic software pipeline that allows students to virtually reconstruct a transparent rolled sheet with printed text on it, the wrapped scroll.

eess.IV↗

arXiv2025

The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity

We deal with Calderón's problem in a layered anisotropic medium $Ω\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $σ=γA$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $Ω$ are fixed and known and that $γ$ is an unknown affine complex-valued function on each layer. We provide Hölder and Lipschitz stability estimates of $σ$ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localised on some open portion $Σ$ of $\partialΩ$, respectively.

math.AP↗

arXiv2023

Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data

We consider the inverse problem of the simultaneous identification of the coefficients $σ$ and $q$ of the equation div$(σ\nabla u) + qu=0$ from the knowledge of the complete Cauchy data pairs. We assume that $σ=γA$ where $A$ is a given matrix function and $γ, q$ are unknown piecewise affine scalar functions. No sign, nor spectrum condition on $q$ is assumed. We derive a result of global Lipschitz stability in dimension $n\geq 3$. The proof relies on the method of singular solutions and on the quantitative estimates of unique continuation.

math.AP↗

arXiv2022

Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional

We address the stability issue in Calderón's problem for a special class of anisotropic conductivities of the form $σ=γA$ in a Lipschitz domain $Ω\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous matrix-valued function and $γ$ is the unknown piecewise affine scalar function on a given partition of $Ω$. We define an ad-hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.

math.AP↗

arXiv2022

Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data

We consider the inverse problem of determining an inclusion contained in a body for a Schrödinger type equation by means of local Cauchy data. Both the body and the inclusion are made by inhomogeneous and anisotropic materials. Under mild a priori assumptions on the unknown inclusion, we establish a logarithmic stability estimate in terms of the local Cauchy data. In view of possible applications, we also provide a stability estimate in terms of an ad-hoc misfit functional.

math.AP↗