Related papers: The Topological Stability Index: A Variance-Based …

We show that certain band gaps, which appear topologically trivial from the perspective of symmetry indicators (SIs), must instead be topological, as guaranteed by real-space information that follows from Topological Quantum Chemistry…

Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…

Power system stability indices are used as measures to evaluate and quantify the response of the system to external large disturbances. This paper provides a comparative analysis of established transient stability indices. The indices…

The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we…

Barcodes form a complete set of invariants for interval decomposable persistence modules and are an important summary in topological data analysis. The set of barcodes is equipped with a canonical one-parameter family of metrics, the…

This paper addresses the problem of real-time monitoring of long-term voltage instability (LTVI) by using local field measurements. Existing local measurement-based methods use Thevenin equivalent parameter estimation that is sensitive to…

In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy.

The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of the space of data, a persistence barcode tracks the evolution of its homological features. In this…

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem…

The short-term voltage stability (SVS) problem in large-scale receiving-end power systems is serious due to the increasing load demand, the increasing use of electronically controlled loads and so on. Some serious blackouts are considered…

Preserving the topology from being inferred by external adversaries has become a paramount security issue for network systems (NSs), and adding random noises to the nodal states provides a promising way. Nevertheless, recent works have…

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…

Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such…

Persistent entropy (PE) is an information-theoretic summary statistic of persistence barcodes that has been widely used to detect regime changes in complex systems. Despite its empirical success, a general theoretical understanding of when…

We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…

Over the past few decades, open source software has been continuously integrated into software supply chains worldwide, drastically increasing reliance and dependence. Because of the role this software plays, it is important to understand…

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…

This paper presents a novel Short-Term Voltage Stability Index (STVSI), which leverages Lyapunov Exponent-based detection to assess and quantify short-term stability triggered by Over Excitation Limiters (OELs) or undamped oscillations in…

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., compound hybrid parameters), and the aggregate behavior…

This paper proposes an approach to address the voltage stability assessment (VSA) considering N-1 contingency. The approach leverages the sensitivity based Thevenin index (STI) which involves evaluating the Jacobian matrix at current…