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There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
Phrase structure trees have a hierarchical structure. In many subjects, most notably in Taxonomy such tree structures have been studied using ultrametrics. Here syntactical hierarchical phrase trees are subject to a similar analysis, which…
This technical report details a family of time warp distances on the set of discrete time series. This family is constructed as an editing distance whose elementary operations apply on linear segments. A specific parameter allows…
Gradient boosted decision trees are some of the most popular algorithms in applied machine learning. They are a flexible and powerful tool that can robustly fit to any tabular dataset in a scalable and computationally efficient way. One of…
Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the…
Sequential lateration is a class of methods for multidimensional scaling where a suitable subset of nodes is first embedded by some method, e.g., a clique embedded by classical scaling, and then the remaining nodes are recursively embedded…
We give a characterization of equilibrium measures for $p$-capacities on the boundary of an infinite tree of arbitrary (finite) local degree. For $p=2$, this provides, in the special case of trees, a converse to a theorem of Benjamini and…
We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…
Traditional text classifiers are limited to predicting over a fixed set of labels. However, in many real-world applications the label set is frequently changing. For example, in intent classification, new intents may be added over time…
The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…
Material microstructures are traditionally compared using sets of statistical measures that are incomplete, e.g., two visually distinct microstructures can have identical grain size distributions and phase fractions. While this is not a…
The same machine learning model running on different edge devices may produce highly-divergent outputs on a nearly-identical input. Possible reasons for the divergence include differences in the device sensors, the device's signal…
We study second order consensus dynamics with random additive disturbances. We investigate three different performance measures: the steady-state variance of pairwise differences between vertex states, the steady-state variance of the…
A distance-based method to reconstruct a phylogenetic tree with $n$ leaves takes a distance matrix, $n \times n$ symmetric matrix with $0$s in the diagonal, as its input and reconstructs a tree with $n$ leaves using tools in combinatorics.…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
A measure of similarity between text embeddings can be considered adequate only if it adheres to the human perception of similarity between texts. In this paper, we introduce the distance-to-distance ratio (DDR), a novel measure of…
Vision-based metric distance and area measurement remains challenging in large-scale outdoor environments due to long-range sensing, camera zoom, and unstable imaging conditions. This work studies planar metric measurement in a real-world…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
A novel delay-based spacing policy for the control of vehicle platoons is introduced together with a notion of disturbance string stability. The delay-based spacing policy specifies the desired inter-vehicular distance between vehicles and…