Related papers: Weighted paths between partitions
This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…
Rand (1971) proposed what has since become a well-known index for comparing two partitions obtained on the same set of units. The index takes a value on the interval between 0 and 1, where a higher value indicates more similar partitions.…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…
In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean subset logic is usually mis-specified as the special case of…
Pairwise network comparison is essential for various applications, including neuroscience, disease research, and dynamic network analysis. While existing literature primarily focuses on comparing entire network structures, we address a…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
The Generalized Hamming weights and their relative version, which generalize the minimum distance of a linear code, are relevant to numerous applications, including coding on the wire-tap channel of type II, $t$-resilient functions,…
An outstanding problem in the theory of nuclear fission is to understand the Hamiltonian dynamics at the scission point. In this work the fissioning nucleus is modeled in self-consistent mean-field theory as a set of Generator Coordinate…
We consider the classical minimum and maximum cut problems: find a partition of vertices of a graph into two disjoint subsets that minimize or maximize the sum of the weights of edges with endpoints in different subsets. It is known that if…