Related papers: Knot data analysis using multiscale Gauss link int…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
The conormal lift of a link $K$ in $\R^3$ is a Legendrian submanifold $\Lambda_K$ in the unit cotangent bundle $U^* \R^3$ of $\R^3$ with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link…
We present a novel method for analyzing geospatial trajectory data using topological data analysis (TDA) to identify a specific class of anomalies, commonly referred to as crop circles, in AIS data. This approach is the first of its kind to…
Data scarcity hinders the usability of data-dependent algorithms when tackling IoT intrusion detection (IID). To address this, we utilise the data rich network intrusion detection (NID) domain to facilitate more accurate intrusion detection…
Neural Networks (GNNs) have revolutionized the molecular discovery to understand patterns and identify unknown features that can aid in predicting biophysical properties and protein-ligand interactions. However, current models typically…
The reliable operation of finite-time quantum heat engines is fundamentally limited by control imperfections that induce nonadiabatic phase accumulation and quantum friction, degrading the stability of the thermodynamic cycle. Traditional…
Anomaly detection in temporal data from sensors under aviation scenarios is a practical but challenging task: 1) long temporal data is difficult to extract contextual information with temporal correlation; 2) the anomalous data are rare in…
Knots and links represent a fundamental motif of non-local connectivity that permeates the physical sciences from string theory to protein folds. While spectral braiding has been explored in two-band non-Hermitian models across various…
High dimensional data can contain multiple scales of variance. Analysis tools that preferentially operate at one scale can be ineffective at capturing all the information present in this cross-scale complexity. We propose a multiscale joint…
Topological data analysis (TDA) uses persistent homology to quantify loops and higher-dimensional holes in data, making it particularly relevant for examining the characteristics of images of cells in the field of cell biology. In the…
This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as clouds of unordered points. In the 0-dimensional case the…
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's…
We propose a novel, good-quality, and less demanding method for detecting knots on the surface of wooden logs using multimodal data fusion. Knots are a primary factor affecting the quality of sawn timber, making their detection fundamental…
Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…
In network link prediction, it is possible to hide a target link from being predicted with a small perturbation on network structure. This observation may be exploited in many real world scenarios, for example, to preserve privacy, or to…
The work for predicting drug and target affinity(DTA) is crucial for drug development and repurposing. In this work, we propose a novel method called GDGRU-DTA to predict the binding affinity between drugs and targets, which is based on…
Knot, link, and tangle theory is crucial in both mathematical theory and practical application, including quantum physics, molecular biology, and structural chemistry. Unlike knots and links, tangles impose more relaxed constraints,…
Topological methods are very rarely used in structural health monitoring (SHM), or indeed in structural dynamics generally, especially when considering the structure and topology of observed data. Topological methods can provide a way of…
A knot theory for two-dimensional square lattice is proposed, which sheds light on design of new two-dimensional material with high topological numbers. We consider a two-band model, focusing on the Hall conductance {\sigma}xy = e^2/hbar*P,…
Graph Domain Adaptation (GDA) addresses a pressing challenge in cross-network learning, particularly pertinent due to the absence of labeled data in real-world graph datasets. Recent studies attempted to learn domain invariant…