Related papers: A Note on Local Ultrametricity in Text

Nonstandard analysis is very complex, so finding a simple description of infinitesimal points will be useful. In this paper, ultrafilters as infinitesimal points in a topological space will be proposed, and some topological concepts is…

How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

In order to utilize identification to the best extent, we need robust and fast algorithms and systems to process the data. Having palmprint as a reliable and unique characteristic of every person, we extract and use its features based on…

A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…

Text spotting in natural scene images is of great importance for many image understanding tasks. It includes two sub-tasks: text detection and recognition. In this work, we propose a unified network that simultaneously localizes and…

Large language models (LLMs) have distinct and consistent stylistic fingerprints, even when prompted to write in different writing styles. Detecting these fingerprints is important for many reasons, among them protecting intellectual…

Characterization of topology and dimensionality of spectral feature spaces provides insight into information content. The objective of this study is to characterize topology and spectral dimensionality of spectral mixing spaces representing…

The use of science to understand its own structure is becoming popular, but understanding the organization of knowledge areas is still limited because some patterns are only discoverable with proper computational treatment of large-scale…

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested…

Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…

Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…

Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…

Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…

We show that there is a fast algorithm that embeds hierarchical structures in three-dimensional Minkowski spacetime. The correlation of data ends up purely encoded in the causal structure. Our model relies solely on oriented token pairs --…

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

This paper presents a scene text detection technique that exploits bootstrapping and text border semantics for accurate localization of texts in scenes. A novel bootstrapping technique is designed which samples multiple 'subsections' of a…

Linguistic feature datasets such as URIEL+ are valuable for modelling cross-lingual relationships, but their high dimensionality and sparsity, especially for low-resource languages, limit the effectiveness of distance metrics. We propose a…