Related papers: A Distance Between Filtered Spaces Via Tripods
We combine the pointed Gromov-Hausdorff metric [Ron10] with the locally $C^0$ distance to obtain the pointed $C^0$-Gromov-Hausdorff distance between maps of possibly different non-compact pointed metric spaces. The latter is then combined…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
If $\Sigma$ and $\Sigma'$ are homotopic embedded surfaces in a $4$-manifold then they may be related by a regular homotopy (at the expense of introducing double points) or by a sequence of stabilisations and destabilisations (at the expense…
The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a…
Information is an inherent component of stochastic processes and to measure the distance between different stochastic processes it is not sufficient to consider the distance between their laws. Instead, the information which accumulates…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
This paper addresses two interrelated problems of the nonlinear filtering mechanism and fast attitude filtering with the matrix Fisher distribution (MFD) on the special orthogonal group. By analyzing the distribution evolution along Bayes'…
We develop a mean-field model to examine the stability of a `quasi-2D suspension' of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by…
Using controlled spinodal decomposition, we have created a fluid-bicontinuous structure stabilized by colloidal particles. We present confocal microscopy studies of these structures and their variation with kinetic pathway. Our studies…
In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
We consider an interesting class of combinatorial symmetries of polytopes which we call \emph{edge-length preserving combinatorial symmetries}. These symmetries not only preserve the combinatorial structure of a polytope but also map each…
We present a generalization of the induced matching theorem and use it to prove a generalization of the algebraic stability theorem for $\mathbb{R}$-indexed pointwise finite-dimensional persistence modules. Via numerous examples, we show…
We use the bailout embeddings of three-dimensional volume-preserving maps to study qualitatively the dy- namics of small spherical neutrally buoyant impurities suspended in a time-periodic incompressible fluid flow. The accumulation of…
In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are…
In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly…
In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a {\it bifurcation phenomena}, we make this explicit in the introduction. In…