Related papers: Inverse Problems in Topological Persistence

There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…

This is an updated survey on the inverse spectral problem written for the Notices of the ICCM. It rapidly reviews some of the material in the previous survey of the same title (arXiv:math/0402356) and then discusses some relatively new…

A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven…

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was…

We study an inverse resonance problem on the line in which we aim at determining a compactly supported and integrable perturbation of a fixed P\"oschl-Teller potential. We define the resonances as the poles of the reflection coefficients…

A topological invariant of the geodesic laminations on a modular surface is constructed. The invariant has a continuous part (the tail of a continued fraction) and a combinatorial part (the singularity data). It is shown, that the invariant…

The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…

A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…

The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has been extended and generalized in various…

In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition.…

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…

This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…

This is the first part of a small-scale explorative study in an effort to start assessing reproducibility issues specific to scientometrics research. This effort is motivated by the desire to generate empirical data to inform debates about…

The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…

The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of…

The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…

Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.

We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…