Related papers: A weighted angle distance on strings
We investigate the velocity-dependent one-scale (VOS) model to the case of one cosmic F-string and two D-strings as color flux tubes in pure Spin($4N$) gauge theory. We analytically calculate the scaling string density as a function of the…
Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…
We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant…
Given a finite directed graph with $n$ vertices, we define a metric $d_G$ on $\mathbb{F}_q^n$, where $\mathbb{F}_q$ is the finite field with $q$ elements. The weight of a word is defined as the number of vertices that can be reached by a…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
We describe some recent progress in understanding and formulating string theory which is based on extensive studies of strings in lower (D=2) dimension. At the center is a large $W_{\infty}$ symmetry that appears most simply in the matrix…
Many applications motivate the distance measure between rankings, such as comparing top-k lists and rank aggregation for voting, and intrigue great interest to researchers. For example, for a search engine, the use of different ranking…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
Economic policy and research rely on the correct evaluation of the billions of high-frequency data points that we collect every day. Consistent clustering algorithms, like DBSCAN, allow us to make sense of the data in a useful way. However,…
We study the inertia of distance matrices of weighted graphs. Our novel congruence-based proof of the inertia of weighted trees extends to a proof for the inertia of weighted unicyclic graphs whose cycle is a triangle. Partial results are…
In this dissertation we study hidden symmetries within the framework of string theory. There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is…
The problem of detecting and measuring the repetitiveness of one-dimensional strings has been extensively studied in data compression and text indexing. Our understanding of these issues has been significantly improved by the introduction…
The M-relative distance, denoted by \rho_M is a generalization of the p-relative distance, which was introduced by Ren-Cang Li. We establish necessary and sufficient conditions under which \rho_M is a metric. In two special cases we derive…
Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…
Graph clustering becomes an important problem due to emerging applications involving the web, social networks and bio-informatics. Recently, many such applications generate data in the form of streams. Clustering massive, dynamic graph…
Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in…
Distance measures have been recognized as one of the fundamental building blocks in time-series analysis tasks, e.g., querying, indexing, classification, clustering, anomaly detection, and similarity search. The vast proliferation of…
This study aims to publish a novel similarity metric to increase the speed of comparison operations. Also the new metric is suitable for distance-based operations among strings. Most of the simple calculation methods, such as string length…
Metric embeddings are central to metric theory and its applications. Here we consider embeddings of a different sort: maps from a set to subsets of a metric space so that distances between points are approximated by minimal distances…