Related papers: Weighted persistent homology for osmolyte molecula…
Existing interpretability methods for Large Language Models (LLMs) predominantly capture linear directions or isolated features. This overlooks the high-dimensional, relational, and nonlinear geometry of model representations. We apply…
Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to perturbations or ability to detect a feature of interest,…
Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology…
Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into machine learning and deep learning models enhances topology awareness and interpretability. However, most PH methods…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
Higher-order properties of functional magnetic resonance imaging (fMRI) induced connectivity have been shown to unravel many exclusive topological and dynamical insights beyond pairwise interactions. Nonetheless, whether these fMRI-induced…
Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…
Here we report the linear viscoelastic properties of amorphous poly(tetramethylene oxide) (PTMO), which is one of the key components in synthesizing segmented polyurethane (PU) elastomers. The temperature and molecular weight dependent…
The relationship between the macroscopic response of the slope and the macrostructure of the force chain network under the action of the metal plate was studied by the particle discrete element method and the persistent homology. The…
This study details an approach for the analysis of social media collected political data through the lens of Topological Data Analysis, with a specific focus on Persistent Homology and the political processes they represent by proposing a…
This paper presents a distributed algorithm on wireless ad-hoc networks that runs in polylogarithmic number of rounds in the size of the network and constructs a linear size, lightweight, (1+\epsilon)-spanner for any given \epsilon > 0. A…
Enhanced stabilisation of protein structures via the presence of inert excipients is a key mechanism adopted both by physiological systems and in biotechnological applications. While the intrinsic stability of proteins is ultimately fixed…
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
Understanding the protein folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the…
Actin cytoskeleton networks generate local topological signatures due to the natural variations in the number, size, and shape of holes of the networks. Persistent homology is a method that explores these topological properties of data and…
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 local hydration around tetrameric Hb in its T$_0$ and R$_4$ conformational substates is analyzed based on molecular dynamics simulations. Analysis of the local hydrophobicity (LH) for all residues at the $\alpha_1 \beta_2$ and $\alpha_2…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…