Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical metric mean...
An augmented metric space is a metric space $(X, d_X)$ equipped with a function $f_X: X \to \mathbb{R}$. This type of data arises commonly in practice, e.g, a point cloud $X$ in $\mathbb{R}^d$ where each point $x\in X$ has a density function value $f...
Let $\mathbf{H}$ be the Cartesian product of a family of finite abelian groups. Via a polynomial approach, we give sufficient conditions for a partition of $\mathbf{H}$ induced by weighted poset metric to be reflexive, which also become necessary for...
Numerical tables are widely used to present experimental results in scientific papers. For table understanding, a metric-type is essential to discriminate numbers in the tables. We introduce a new information extraction task, metric-type identificati...
Recently, Chen and Sbert proposed a general divergence measure. This report presents some interim findings about the question whether the divergence measure is a metric or not. It has been postulated that (i) the measure might be a metric when (0 < k...
The assessment of evaluation metrics (meta-evaluation) is crucial for determining the suitability of existing metrics in text-to-image (T2I) generation tasks. Human-based meta-evaluation is costly and time-intensive, and automated alternatives are sc...
The theory of massive gravity possesses ambiguities when the spacetime metric evolves far from the non-dynamical fiducial metric used to define it. We explicitly construct a spherically symmetric example case where the metric evolves to a coordinate-...
Deep metric learning algorithms have a wide variety of applications, but implementing these algorithms can be tedious and time consuming. PyTorch Metric Learning is an open source library that aims to remove this barrier for both researchers and prac...
The smallest set of vertices needed to differentiate or categorize every other vertex in a graph is referred to as the graph's metric dimension. Finding the class of graphs for a particular given metric dimension is an NP-hard problem. This concept h...
The "metric" structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not determine a uni...
Recently Bingbing Liang and Hanfeng Li computed the mean dimension and metric mean dimension for algebraic actions of amenable groups. We show how to extend their computation of metric mean dimension to the case of sofic groups, provided that the dua...
Apr 3, 2025 · What are Metrics? Metrics are numbers that tell you important information about a process under question. They tell you accurate measurements about how the process is functioning and …
We introduce \emph{Metric-Fair Prompting}, a fairness-aware prompting framework that guides large language models (LLMs) to make decisions under metric-fairness constraints. In the application of multiple-choice medical question answering, each {(que...
Metrics examples (⭐ 2)
This is an invitation to the probabilistic approach for constructing Kähler-Einstein metrics on complex projective algebraic manifolds X. The metrics in question emerge in the large N-limit from a canonical way of sampling N points on X, i.e. from r...
Puma plugin to export puma stats as prometheus metrics (⭐ 119)
We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to $\mathbb R^n$ equipped with a distance $(d_{\rm E})^ε$, for some $n\in \mathbb N_0$ and $ε\in (0,1]$, where $d_{\rm E}$ is the Euclidean dis...
We prove a generalization of Tyson-Wu's characterization of metric spaces biLipschitz equivalent to snowflakes to every metric space, by removing compactness, doubling and embeddability assumptions. We also characterize metric spaces that are biLipsc...
Metrica Sports sample tracking and event data (⭐ 451)
Exporter that reads metrics for SR-IOV Virtual Functions and exposes them in the Prometheus format. (⭐ 26)