Related papers: Atom-specific persistent homology and its applicat…
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…
Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a…
Given the amino acid sequence of a protein, researchers often infer its structure and function by finding homologous, or evolutionarily-related, proteins of known structure and function. Since structure is typically more conserved than…
By general case we mean methods able to process simplicial sets and chain complexes not of finite type. A filtration of the object to be studied is the heart of both subjects persistent homology and spectral sequences. In this paper we…
Most of the current understanding of structure-property relations at the molecular and the supramolecular scales can be formulated in terms of the stability of and the interactions between a limited number of recurring structural motifs…
Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and backpropagate gradients only onto the simplices involved in…
Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been…
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistence modules -- graded modules over $\kk[t]$ is an important…
A method to search for local structural similarities in proteins at atomic resolution is presented. It is demonstrated that a huge amount of structural data can be handled within a reasonable CPU time by using a conventional relational…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
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…
The local structure of a protein strongly impacts its function and interactions with other molecules. Therefore, a concise, informative representation of a local protein environment is essential for modeling and designing proteins and…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called persistence complex is used to reveal…
Magnitude homology is an emerging framework that captures the intrinsic topological and geometric features of metric spaces, demonstrating significant potential for topoplogical data analysis and geometric data analysis. This work…
Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…
This paper is a cursory study on how topological features are preserved within the internal representations of neural network layers. Using techniques from topological data analysis, namely persistent homology, the topological features of a…
We present a topology-informed approach for classifying particle jets using persistent homology, a framework that captures the structural properties of point clouds. Particle jets produced in proton-proton collisions consist of cascades of…