Related papers: A Note on Local Ultrametricity in Text
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
Hypernym discovery is the problem of finding terms that have is-a relationship with a given term. We introduce a new context type, and a relatedness measure to differentiate hypernyms from other types of semantic relationships. Our Document…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
The semantic similarity between documents of a text corpus can be visualized using map-like metaphors based on two-dimensional scatterplot layouts. These layouts result from a dimensionality reduction on the document-term matrix or a…
In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 U.S. cities and a few more from elsewhere of different sizes. It is found that all the…
Network data enriched with textual information, referred to as text networks, arise in a wide range of applications, including email communications, scientific collaborations, and legal contracts. In such settings, both the structure of…
It is shown that a locally finite ultrametric space $(X, d)$ is generated by labeled tree if and only if, for every open ball $B \subseteq X$, there is a point $c \in B$ such that $d(x, c) = \operatorname{diam} B$ whenever $x \in B$ and $x…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
The statistical methods derived and described in this thesis provide new ways to elucidate the structural properties of text and other symbolic sequences. Generically, these methods allow detection of a difference in the frequency of a…
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
Human syntactic structures are usually represented as graphs. Much research has focused on the mapping between such graphs and linguistic sequences, but less attention has been paid to the shapes of the graphs themselves: their topologies.…
We describe the class of graphs for which all metric spaces with diametrical graphs belonging to this class are ultrametric. It is shown that a metric space $(X, d)$ is ultrametric iff the diametrical graph of the metric $d_{\varepsilon}(x,…
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Embedded topic models are able to learn interpretable topics even with large and heavy-tailed vocabularies. However, they generally hold the Euclidean embedding space assumption, leading to a basic limitation in capturing hierarchical…
The rapid advancements in large language models (LLMs) have significantly improved their ability to generate natural language, making texts generated by LLMs increasingly indistinguishable from human-written texts. While recent research has…
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…
Understanding the spatial networks formed by the trajectories of mobile users can be beneficial to applications ranging from epidemiology to local search. Despite the potential for impact in a number of fields, several aspects of human…