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Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…

Machine Learning · Computer Science 2026-03-12 Eng-Jon Ong , Omer Bobrowski , Gesine Reinert , Primoz Skraba

This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…

Numerical Analysis · Mathematics 2024-09-18 Johannes Pfefferer , Boris Vexler

This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…

Machine Learning · Computer Science 2021-01-05 Maciej Skorski

A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…

Analysis of PDEs · Mathematics 2020-07-14 Giuseppe Buttazzo , Francesco Paolo Maiale

Lower bounds are obtained on the maximum field strength in one or both phases in a body containing two-phases. These bounds only incorporate boundary data that can be obtained from measurements at the surface of the body, and thus may be…

The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the…

Numerical Analysis · Mathematics 2016-07-04 Nuutti Hyvönen , Vesa Kaarnioja , Lauri Mustonen , Stratos Staboulis

The multifrequency electrical impedance tomography consists in retrieving the conductivity distribution of a sample by injecting a finite number of currents with multiple frequencies. In this paper we consider the case where the…

Numerical Analysis · Mathematics 2017-04-18 Habib Ammari , Faouzi Triki , Chun-Hsiang Tsou

The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of…

Optimization and Control · Mathematics 2015-04-10 Abdul Wahab

We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…

Geophysics · Physics 2009-05-05 R. B. Schlottmann

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…

Optimization and Control · Mathematics 2022-09-27 Paul R. Arbic , Vladislav Bukshtynov

In high-contrast composite materials, the electric (or stress) field may blow up in the narrow region between inclusions. The gradient of solutions depend on $\epsilon$, the distance between the inclusions, where $\epsilon$ approaches to…

Analysis of PDEs · Mathematics 2026-04-22 Linjie Ma

The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…

Medical Physics · Physics 2024-12-17 Sarah J. Hamilton , Peter Muller , Ville Kolehmainen , Jussi Toivanen

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current.…

Analysis of PDEs · Mathematics 2012-02-27 Giovanni Alessandrini , Antonio Bilotta , Antonino Morassi , Edi Rosset , Emilio Turco

We improve both dimension compression and expansion bounds for homeomorphisms with $p$-exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to…

Complex Variables · Mathematics 2022-03-25 Lauri Hitruhin

This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic…

Differential Geometry · Mathematics 2012-04-03 Ulrich Menne

In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in $\mathbb{R}^n, n\ge 2$. For these two extreme cases of the conductivity problems, the gradients of their…

Analysis of PDEs · Mathematics 2009-09-23 Ellen ShiTing Bao , YanYan Li , Biao Yin

We consider the characterization of entanglement depth in a quantum many-body system from the device-independent perspective; i.e., certifying how many particles are genuinely entangled without relying on assumptions on the system itself…

This work extends the results of [Garde and Hyv\"onen, Math. Comp. 91:1925-1953] on series reversion for Calder\'on's problem to the case of realistic electrode measurements, with both the internal admittivity of the investigated body and…

Numerical Analysis · Mathematics 2023-07-19 Henrik Garde , Nuutti Hyvönen , Topi Kuutela

In practical applications of quantum information science, quantum systems can have non-negligible interactions with the environment, and this generally degrades the power of quantum protocols as it introduces noise. Counteracting this by…

Quantum Physics · Physics 2014-10-10 Filippo M. Miatto , Kevin Piché , Thomas Brougham , Robert W. Boyd

Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and…

Numerical Analysis · Mathematics 2018-11-19 Bastian Harrach , Marcel Ullrich