Related papers: Topological Analysis of Syntactic Structures
Force-directed layouts belong to a popular class of methods used to position nodes in a node-link diagram. However, they typically lack direct consideration of global structures, which can result in visual clutter and the overlap of…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
It is commonly believed that knowledge of syntactic structure should improve language modeling. However, effectively and computationally efficiently incorporating syntactic structure into neural language models has been a challenging topic.…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
Syntactic discontinuity is a grammatical phenomenon in which a constituent is split into more than one part because of the insertion of an element which is not part of the constituent. This is observed in many languages across the world…
The network characteristics based on the phonological similarities in the lexicons of several languages were examined. These languages differed widely in their history and linguistic structure, but commonalities in the network…
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…
Strategic diagrams and co-word analysis are widely employed to examine the conceptual structure of scientific domains and their development over time. Yet a structural inconsistency characterises dominant longitudinal implementations:…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…