arXiv research

Paper introduces MJ distances for better anomaly detection in time series.

Surjectivity of Cannon-Thurston map proven for metric graph bundles.

Study identifies and validates a method for system identification of Markov jump linear systems.

The article extends Thurston's Grafting Theorem to signed spaces and defines a framed monodromy map.

Study shows ethanol blends and incentives can significantly reduce transportation carbon emissions.

New examples show some convex-cocompact subgroups are separable.

Let $1 \to H \to G \to Q \to 1$ be an exact sequence where $H= π_1(S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is finitely generated free. The aim of this paper is to provide sufficient conditions to prove that $G$ is cubulable and construct examples satis…

Constructs a universal Cannon-Thurston map for a new curve complex.

Mahan Mitra (Mj) proved Cannon--Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group. We prove that Cannon--Thurston maps do not exist for infinite normal hyperbolic subgroups of non-hyperbolic CAT(0) groups with isolated flats with respect to the visual boundaries. We also show Cannon--Thurston ma…

This paper tackles adaptive control of unknown Markov jump systems with sample complexity and regret bounds.

Study of graphs interpolating curve and pants graphs, providing formulae and geometry classifications.

When 1 -> H -> G -> Q -> 1 is a short exact sequence of three infinite, word-hyperbolic groups, Mahan Mitra (Mj) has shown that the inclusion map from H to G extends continuously to a map between the Gromov boundaries of H and G. This boundary map is known as the Cannon-Thurston map. In this context, Mitra associates t…

We study the closed group of homeomorphisms of the boundary of real hyperbolic space generated by a cocompact Kleinian group $G_1$ and a quasiconformal conjugate $h^{-1}G_2 h$ of a cocompact group $G_2$. We show that if the conjugacy $h$ is not conformal then this group contains a non-trivial one parameter subgroup. Th…

A brain-inspired spiking Transformer reduces energy consumption and enhances interpretability.

The paper tightens bounds on distances between Reeb graphs.

Extends Teichmüller distance concept to non-distance maps.

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the Wasserstein distance, while being much simpler to compute, and is therefore used in vario…

We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics whenever the ground distance between the marginals is a metric, generalize both…

In the present paper we calculate the Gromov-Hausdorff distance between an arbitrary simplex (a metric space all whose non-zero distances are the same) and a finite metric space whose non-zero distances take two distinct values (so-called $2$-distance spaces). As a corollary, a complete solution to generalized Borsuk p…

New toolkit for directed distances improves flexibility of OT problems.

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 that the above-mentioned common distances in many situations fail to take into ac…

Graph neural network learns graph distances effectively.

A new robust metric compares distributions more accurately than existing methods.

A new metric HCP distance for comparing distributions.

Formula for interleaving distance of rectangle persistence modules.

New distances measure mixtures of Gaussians, useful in machine learning.

New distances for comparing multivariate normal distributions.

The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.

Finite mapping class groups for Heegaard splittings with distance ≥ 3, but not for distance 2.

Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering often rely on some distance or similarity measure. It is of tremendous importance t…

The paper studies horofunction compactifications of symmetric cones under Finsler distances.

A new supervised tree-Wasserstein distance improves document classification.

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using generalized Gini distance, an energy distance in reproducing kernel Hilbert spaces (RK…

CADM proposes a cluster-specific distance metric for categorical data clustering.

Estimates manifold distances using graph Laplacian, proving consistency.

Transforms distance-based outlier scores into interpretable probabilistic estimates.

New distances defined on Legendrian spaces without positive loops.

A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions, wherein each component is a distance-squared function. In this paper, compositions of…

A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.

The study bounds distances in simplicial complexes and defines new invariants for 3-manifolds and handlebody-knots.

The literature postulates that the dynamic time warping (dtw) distance can cope with temporal variations but stores and processes time series in a form as if the dtw-distance cannot cope with such variations. To address this inconsistency, we first show that the dtw-distance is not warping-invariant. The lack of warpin…

The distance function $\varrho(p,q)$ (or $d(p,q)$) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over $\mathbb R^n$, whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no F…

We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerica…

Using Blanchfield pairings, we show that two Alexander polynomials cannot be realized by a pair of matrices with Gordian distance one if a corresponding quadratic equation does not have an integer solution. We also give an example of how our results help in calculating the Gordian distances, algebraic Gordian distances…

The paper explores selecting the parameter α for Fermat distance to balance geometry and noise.

The paper introduces a statistical distance matrix for better feature representation and clustering.

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…

Differentially private data structures for estimating distances between strings.