相关论文: Steinhaus Filtration and Stable Paths in the Mappe…

Steganography represents the art of unobtrusively concealing a secrete message within some cover data. The key scope of this work is about visual steganography techniques that hide a full-sized color image / video within another. A majority…

Two important tasks in the field of Topological Data Analysis are building practical multifiltrations on objects and using TDA to detect the geometry. Motivated by the tasks, we build multiparameter filtrations by operators on images named…

We strengthen the usual stability theorem for Vietoris-Rips (VR) persistent homology of finite metric spaces by building upon constructions due to Usher and Zhang in the context of filtered chain complexes. The information present at the…

Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear equipped with a real valued function. Persistence is a…

Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the available topological data analysis toolboxes. Other issues…

Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework.…

Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…

We propose a modification of the Mapper algorithm that removes the assumption of a single resolution scale across semantic space and improves the robustness of the results under change of parameters. Our work is motivated by datasets where…

Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…

Autonomous robots are increasingly deployed for information-gathering tasks in environments that vary across space and time. Planning informative and safe trajectories in such settings is challenging because information decays when regions…

We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…

Machine learning models are increasingly applied to biomedical data, yet their adoption in high stakes domains remains limited by poor robustness, limited interpretability, and instability of learned features under realistic data…

Distances have a ubiquitous role in persistent homology, from the direct comparison of homological representations of data to the definition and optimization of invariants. In this article we introduce a family of parametrized pseudometrics…

We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \mapsto -x$. This system exhibits a Turing instability and we…

A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we…

We introduce the persistence heatmap, a parametrized summary based on representative cycles in persistence diagrams, designed to enhance stability and explainability in topological data analysis. Algorithms to compute persistence diagrams…

Stiefel-Whitney classes are invariants of the tangent bundle of a smooth manifold, represented as cohomology classes of the base manifold. These classes are essential in obstruction theory, embedding problems, and cobordism theory. In this…

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in…

It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…

We consider a general stable flow problem in a directed and capacitated network, where each vertex has a strict preference list over the incoming and outgoing edges. A flow is stable if no group of vertices forming a path can mutually…