Related papers: Topological signature for periodic motion recognit…

We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…

We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…

Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In…

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…

The global topology of spacetime, though invisible to local curvature measurements, leaves signatures on the correlation functions of quantum fields. We study these signatures using an Unruh-DeWitt particle detector operating in…

An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…

Object recognition in unseen indoor environments remains a challenging problem for visual perception of mobile robots. In this letter, we propose the use of topologically persistent features, which rely on the objects' shape information, to…

Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models.…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…

Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. We lift the theory of path signatures to the setting of Lie group…

Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply the Fels-Olver's moving frame method (for geometric features) paired with…

Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…

The signature of a path is an essential object in the theory of rough paths. The signature representation of the data stream can recover standard statistics, e.g. the moments of the data stream. The classification of random walks indicates…

Over the years, hand gesture recognition has been mostly addressed considering hand trajectories in isolation. However, in most sign languages, hand gestures are defined on a particular context (body region). We propose a pipeline to…

Detecting statistical interactions between input features is a crucial and challenging task. Recent advances demonstrate that it is possible to extract learned interactions from trained neural networks. It has also been observed that, in…

Gait event detection of the initial contact and toe off is essential for running gait analysis, allowing the derivation of parameters such as stance time. Heuristic-based methods exist to estimate these key gait events from tibial…

We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…