Related papers: Topology reconstruction for asymmetric systems by …
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according…
The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological…
In this article, we present a novel approach to reconstruct the topology of networked linear dynamical systems with latent nodes. The network is allowed to have directed loops and bi-directed edges. The main approach relies on the unique…
Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…
The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts…
We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
Algebraic topology (homology) is used to analyze the weakly turbulent state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Benard convection.The analysis reveals topological asymmetries that…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
(This is a report for the Proceedings of ``Journees Relativistes 1993'' written in September 1993. Containes a short description of the results published elsewhere in the joint paper with A. Ashtekar) Integral calculus on the space of gauge…
Topology plays an important role in non-hermitian systems. How to characterize a non-hermitian topological system under open-boundary conditions(OBCs) is a challenging problem. A one-dimensional(1D) topological invariant defined on a…
In this paper we propose a new method to enhance a mapping $\mu(\cdot)$ of a parallel application's computational tasks to the processing elements (PEs) of a parallel computer. The idea behind our method \mswap is to enhance such a mapping…
We study a one-parameter family of time-reversible Hamiltonian vector fields in $\mathbb{R}^4$, which has received great attention in the literature. On the one hand, it is due to the role it plays in the context of certain applications in…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…