相关论文: Distance statistics in quadrangulations with no mu…

We consider quadrangulations with a boundary and derive explicit expressions for the generating functions of these maps with either a marked vertex at a prescribed distance from the boundary, or two boundary vertices at a prescribed mutual…

We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…

We compute the distance-dependent two-point function of vertex-bicolored planar maps, i.e., maps whose vertices are colored in black and white so that no adjacent vertices have the same color. By distance-dependent two-point function, we…

We compute the generating function of random planar quadrangulations with three marked vertices at prescribed pairwise distances. In the scaling limit of large quadrangulations, this discrete three-point function converges to a simple…

We present a new derivation of the distance-dependent two-point function of random planar triangulations. As it is well-known, this function is intimately related to the generating functions of so-called slices, which are pieces of…

We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have…

In this paper, we consider the following query problem: given two weighted point sets $A$ and $B$ in the Euclidean space $\mathbb{R}^d$, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than…

In the dynamical triangulation model of 4D euclidean quantum gravity we measure two-point functions of the scalar curvature as a function of the geodesic distance. To get the correlations it turns out that we need to subtract a squared…

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…

We study the fractal structure of the surface in two-dimensional quantum Regge calculus by performing Monte Carlo simulation with up to 200,000 triangles. The result can be compared with the universal scaling function obtained analytically…

We present a new derivation of the distance-dependent two-point function for planar Eulerian triangulations and give expressions for more refined generating functions where we also control hull perimeters. These results are obtained in the…

Let $M_n$ be a simple triangulation of the sphere $S^2$, drawn uniformly at random from all such triangulations with n vertices. Endow $M_n$ with the uniform probability measure on its vertices. After rescaling graph distance on $V(M_n)$ by…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…

Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…

We show that if a disc triangulation has all internal vertex degrees at least 6, then the full triangulation may be determined from the pairwise graph distance between boundary vertices. A similar result holds for quadrangulations with all…

Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations…

The large-scale statistics of observables such as the galaxy density are chiefly determined by their dependence on the local coarse-grained matter density. This dependence can be measured directly and efficiently in N-body simulations by…

Cosmological distances as a function of redshift depend on the effective curvature density via the effect on the geometrical path of photons from large scale spatial curvature and its effect on the expansion history, H(z). Cosmological…

We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x…