Related papers: Topological Analysis of Syntactic Structures
Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures. The two main sources of syntactic data are the SSWL database…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
We study the global topology of the syntactic and semantic distributional similarity networks for English through the technique of spectral analysis. We observe that while the syntactic network has a hierarchical structure with strong…
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…
The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…
We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…
In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between…
The theory of persistence modules is an emerging field of algebraic topology which originated in topological data analysis. In these notes we provide a concise introduction into this field and give an account on some of its interactions…
We investigate the large-scale structure and temporal evolution of cyclonic and anticyclonic systems in the North Atlantic using persistent homology applied to daily sea-level pressure anomalies from the ERA5 reanalysis (1950-2022). By…
We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…
This paper introduces how human languages can be studied in light of recent development of network theories. There are two directions of exploration. One is to study networks existing in the language system. Various lexical networks can be…
Investigating linguistic relationships on a global scale requires analyzing diverse features such as syntax, phonology and prosody, which evolve at varying rates influenced by internal diversification, language contact, and sociolinguistic…
We introduce a novel set of observables associated to the rapidly developing field of persistent homology for the quantitative characterization of nuclear collisions and their evolution. Persistent homology allows for the identification of…
Typological databases in linguistics are usually categorical-valued. As a result, it is difficult to have a clear visualization of the data. In this paper, we describe a workflow to analyze the topological shapes of South American languages…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology.…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…