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Recent years have witnessed a fast growth in mathematical artificial intelligence (AI). One of the most successful mathematical AI approaches is topological data analysis (TDA) via persistent homology (PH) that provides explainable AI (xAI)…
The weight of links in a network is often related to the similarity of the nodes. Here, we introduce a simple tunable measure for analysing the similarity of nodes across different link weights. In particular, we use the measure to analyze…
Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
AI-native wireless receivers based on deep learning exhibit remarkable performance under stationary channel conditions, yet their resilience to distributional shifts remains poorly characterized by conventional metrics such as bit error…
Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
Ab initio molecular dynamics simulations of liquid water under equilibrium ambient conditions, together with a novel energy decomposition analysis, have recently shown that a substantial fraction of water molecules exhibit a significant…
This paper, the fourth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the intricate challenge of distributed heterogeneous multisensor multitarget…
In this work we examine the effect of R=[NCO]/[OH] in the R=<1 regime, on the resultant structural topology of polybutadiene polyurethane (PBPU) elastomer networks based on hydroxy-terminated polybutadiene (HTPB). We employ…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
Aqueous solubility and partition coefficient are important physical properties of small molecules. Accurate theoretical prediction of aqueous solubility and partition coefficient plays an important role in drug design and discovery. The…
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…
Artificial intelligence-assisted drug design is revolutionizing the pharmaceutical industry. Effective molecular features are crucial for accurate machine learning predictions, and advanced mathematics plays a key role in designing these…
Elastic network models (ENM) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have…