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

We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…

We use the Minimal Spanning Tree to characterize the aggregation level of given sets of points. We test 3 distances based on the histogram of the MST edges to discriminate between the distributions. We calibrate the method by using…

We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite…

The signaling dimension of any given physical system represents its classical simulation cost, that is, the minimum dimension of a classical system capable of reproducing all the input/output correlations of the given system. The signaling…

We define the model of two-dimensional random interlacements using simple random walk trajectories conditioned on never hitting the origin, and then obtain some properties of this model. Also, for random walk on a large torus conditioned on…

Computing the quadratic transportation metric (also called the $2$-Wasserstein distance or root mean square distance) between two point clouds, or, more generally, two discrete distributions, is a fundamental problem in machine learning,…

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…

Given a metric space $(X,d_X)$, the earth mover distance between two distributions over $X$ is defined as the minimum cost of a bipartite matching between the two distributions. The doubling dimension of a metric $(X, d_X)$ is the smallest…

We apply the Minkowski Tensor statistics to two dimensional slices of the three dimensional density field. The Minkowski Tensors are a set of functions that are sensitive to directionally dependent signals in the data, and furthermore can…

We propose a novel technique to probe the expansion history of the Universe based on the clustering statistics of cosmic voids. In particular, we compute their two-point statistics in redshift space on the basis of realistic mock galaxy…

We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…

In this paper, the problem of computing the projection, and therefore the minimum distance, from a point onto a Minkowski sum of general convex sets is studied. Our approach is based on the minimum norm duality theorem originally stated by…

The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact computation of this distance would permit multi-parameter…

Let $D$ denote the distance matrix for an $n+1$ point metric space $(X,d)$. In the case that $X$ is an unweighted metric tree, the sum of the entries in $D^{-1}$ is always equal to $2/n$. Such trees can be considered as affinely independent…

The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…

For the classical space of functions with bounded mean oscillation, it is well known that VMO** = BMO and there are many characterizations of the distance from a function f in BMO to VMO. When considering the Bloch space, results in the…

We present a new approach to scalable quantum computing--a ``qubus computer''--which realises qubit measurement and quantum gates through interacting qubits with a quantum communication bus mode. The qubits could be ``static'' matter qubits…

Classical multidimensional scaling (CMDS) is a technique that embeds a set of objects in a Euclidean space given their pairwise Euclidean distances. The main part of CMDS involves double centering a squared distance matrix and using a…

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…

Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background…