相关论文: Persistent Topology of Syntax
Persistence diagrams, which summarize the birth and death of homological features extracted from data, are employed as stable signatures for applications in image analysis and other areas. Besides simply considering the multiset of…
Persistent homology typically studies the evolution of homology groups $H_p(X)$ (with coefficients in a field) along a filtration of topological spaces. $A_\infty$-persistence extends this theory by analysing the evolution of subspaces such…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
Recurrent neural network grammars (RNNGs) are generative models of (tree,string) pairs that rely on neural networks to evaluate derivational choices. Parsing with them using beam search yields a variety of incremental complexity metrics…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and its associated water hydrogen-bonding networks still remains a challenging…
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensional persistence modules and…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the…
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 homology is a tool used to measure topological features that are present in data sets and functions. Persistence pairs births and deaths of these features as we iterate through the sublevel sets of the data or function of…
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…
The structure of topology underpins much of the research on performance and robustness, yet available topology data are typically scarce, necessitating the generation of synthetic graphs with desired properties for testing or release. Prior…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer…
This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…
Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at multiple scales is of particular interest. A major obstacle to…
Classical persistent homology is a powerful mathematical tool for shape comparison. Unfortunately, it is not tailored to study the action of transformation groups that are different from the group Homeo(X) of all self-homeomorphisms of a…