Related papers: Multiparameter Persistent Homology for Molecular P…

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…

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…

Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of…

Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…

A method is presented for the distributed computation of persistent homology, based on an extension of the generalized Mayer-Vietoris principle to filtered spaces. Cellular cosheaves and spectral sequences are used to compute global…

Predicting molecular properties (e.g., atomization energy) is an essential issue in quantum chemistry, which could speed up much research progress, such as drug designing and substance discovery. Traditional studies based on density…

Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…

Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability…

SMILES is a linear representation of chemical structures which encodes the connection table, and the stereochemistry of a molecule as a line of text with a grammar structure denoting atoms, bonds, rings and chains, and this information can…

We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…

Structural fingerprints and pharmacophore modeling are methodologies that have been used for at least two decades in various fields of cheminformatics: from similarity searching to machine learning (ML). Advances in silico techniques…

Advancements in neural machinery have led to a wide range of algorithmic solutions for molecular property prediction. Two classes of models in particular have yielded promising results: neural networks applied to computed molecular…

We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…

Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large…

In this paper, a Feature-preserving Particle Generation (FPPG) method for arbitrary complex geometry is proposed. Instead of basing on implicit geometries, such as level-set, FPPG employs an explicit geometric representation for the…

Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address…

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single…

3-D shape is important to chemistry, but how important? Machine learning works best when the inputs are simple and match the problem well. Chemistry datasets tend to be very small compared to those generally used in machine learning so we…

The shape of a molecule determines its physicochemical and biological properties. However, it is often underrepresented in standard molecular representation learning approaches. Here, we propose using the Euler Characteristic Transform…