相关论文: Topology from the Bottom Up

In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…

Patient-specific 3D printing of congenital heart anatomy demands an accurate segmentation of the thin tissue interfaces which characterise these diagnoses. Even when a label set has a high spatial overlap with the ground truth, inaccurate…

The goal of this article is to survey recent developments in the theory of contact structures in dimension three.

This is an account of one man's view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological…

We investigate the {\it topography\/} of the \o3 vacuum after various degrees of under-relaxed cooling, using the na\"{\i}ve action density and geometric and field theoretical definitions of the topological charge density. The results are…

In architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements…

In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…

These short notes are meant as a quick reference for the construction of SLR(1), of LR(1), and of LALR(1) parsing tables.

This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…

This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.

Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM)…

The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima…

We survey work on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M with boundary. The interior of AH(M) is quite well-understood, but the topology of the entire space…

Over the years, scene understanding has attracted a growing interest in computer vision, providing the semantic and physical scene information necessary for robots to complete some particular tasks autonomously. In 3D scenes, rich spatial…

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany…

We consider exactly solvable models in (3+1)d whose ground states are described by topological lattice gauge theories. Using simplicial arguments, we emphasize how the consistency condition of the unitary map performing a local change of…

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are…

The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…

The scenario of a cosmology with topological defects is surveyed starting from the field theoretic aspects and ending with a description of large-scale structure formation and magnetic field generation. (Lectures delivered at ICTP, Trieste,…