相关论文: Geodesic Distance in Planar Graphs: An Integrable …
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank invariants), is among the most studied metrics in this context,…
The concept of $n$-distance was recently introduced to generalize the classical definition of distance to functions of $n$ arguments. In this paper we investigate this concept through a number of examples based on certain geometrical…
The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$.…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
Graph Generating Dependencies (GGDs) informally express constraints between two (possibly different) graph patterns which enforce relationships on both graph's data (via property value constraints) and its structure (via topological…
We explore a connection between geodesic nets and quantum graphs optimising certain functionals from spectral theory. For surfaces, critical metrics for the normalised $k^{\mathrm{th}}$ eigenvalue of the Laplacian give rise to isometric…
Starting from the framework defined by Matveev and Shevchishin we derive the local and the global structure for the four types of super-integrable Koenigs metrics. These dynamical systems are always defined on non-compact manifolds, namely…
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
We obtain first order linear partial differential equations which are satisfied by exponential generating functions of two variables for the number of connected bipartite graphs with given Betti number. By solving these equations…
In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
The inverse geodesic length of a graph $G$ is the sum of the inverse of the distances between all pairs of distinct vertices of $G$. In some domains it is known as the Harary index or the global efficiency of the graph. We show that, if $G$…
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs
We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…