相关论文: Tension continuous maps--their structure and appli…
The central theorem of topological graph theory states that the graph minor relation is a well-quasi-order on graphs. It has far-reaching consequences, in particular in the study of graph structures and the design of (parameterized)…
We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
Network alignment task, which aims to identify corresponding nodes in different networks, is of great significance for many subsequent applications. Without the need for labeled anchor links, unsupervised alignment methods have been…
In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$. The spectrum of $G$ is referring to its adjacency…
The union of a directed family of topological groups can be equipped with two noteworthy topologies: the finest topology making each injection continuous, and the finest group topology making each injection continuous. This begs the…
The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of…
Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite…
Magnitude and (co)weightings are quite general constructions in enriched categories, yet they have been developed almost exclusively in the context of Lawvere metric spaces. We construct a meaningful notion of magnitude for flow graphs…
A relational structure is (connected-)homogeneous if every isomorphism between finite (connected) substructures extends to an automorphism of the structure. We investigate notions which generalise (connected-)homogeneity, where…
The systematic study of Tur\'an-type extremal problems for edge-ordered graphs was initiated by Gerbner et al. in 2020. Here we characterize connected edge-ordered graphs with linear extremal functions and show that the extremal function of…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
This work presents some outcomes of a theoretical investigation of incompressible high-order networks defined by a generalized graph representation. We study some of their network topological properties and how these may be related to…
Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…
We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the…
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…