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Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…

We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into…

Topological Data Analysis (TDA), a relatively new field of data analysis, has proved very useful in a variety of applications. The main persistence tool from TDA is persistent homology in which data structure is examined at many scales.…

Unravelling the block structure of a network is critical for studying macroscopic features and community-level dynamics. The weighted stochastic block model (WSBM), a variation of the traditional stochastic block model, is designed for…

Recent advances in spatial and temporal networks have enabled researchers to more-accurately describe many real-world systems such as urban transport networks. In this paper, we study the response of real-world spatio-temporal networks to…

We present a machine learning approach that leverages persistent homology to classify bacterial flagellar motors into two functional states: rotated and stalled. By embedding protein structural data into a topological framework, we extract…

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…

Data analysis that uses the output of topological data analysis as input for machine learning algorithms has been the subject of extensive research. This approach offers a means of capturing the global structure of data. Persistent homology…

In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks. Betti matching loss builds on techniques from topological data…

This paper presents a density-based topology optimization method for designing three-dimensional (3D) compliant mechanisms and loadbearing structures with design-dependent pressure loading. Instead of interface-tracking techniques, the…

The nature of the atomic defects on the hydrogen passivated Si (100) surface is analyzed using deep learning and scanning tunneling microscopy (STM). A robust deep learning framework capable of identifying atomic species, defects, in the…

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…

Recently, there has been a growing concern about the overload status of the power grid networks, and the increasing possibility of cascading failures. Many researchers have studied these networks to provide design guidelines for more robust…

We address the problem of safety verification for nonlinear stochastic systems, specifically the task of certifying that system trajectories remain within a safe set with high probability. To tackle this challenge, we adopt a set-erosion…

Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…

Controlling structural complexity, particularly the number of holes, remains a fundamental challenge in topology optimization, with significant implications for both theoretical analysis and manufacturability. Most existing approaches rely…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

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,…

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…