相关论文: Jacobi Set Simplification for Tracking Topological…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…

In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of…

We present a holistic, topology-based visualization technique for spatial time series data based on an adaptation of Fuzzy Contour Trees. Common analysis approaches for time dependent scalar fields identify and track specific features. To…

Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…

We study the problem of detecting the onset of path splitting in stochastic interpolation between probability distributions. This question is especially subtle when the target distribution is nonconvex or supported on disconnected…

We study a class of weakly coupled systems of Hamilton{Jacobi equations at the critical level. We associate to it a family of scalar discounted equation. Using control{theoretic tech- niques we construct an algorithm which allows obtaining…

Feature tracking is a common task in visualization applications, where methods based on topological data analysis (TDA) have successfully been applied in the past for feature definition as well as tracking. In this work, we focus on…

In this second paper of the series we specify general theory developed in the first paper. Here we study the structure of Jacobi fields in the case of an analytic system and piece-wise analytic control. Moreover, we consider only…

We describe methods of estimating the entire Lyapunov spectrum of a spatially extended system from multivariate time-series observations. Provided that the coupling in the system is short range, the Jacobian has a banded structure and can…

This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse temporal sampling of the corresponding scalar fields, denoted…

We present local biplots, a an extension of the classic principal components biplot to multi-dimensional scaling. Noticing that principal components biplots have an interpretation as the Jacobian of a map from data space to the principal…

It remains a huge challenge to design effective and efficient trackers under complex scenarios, including occlusions, illumination changes and pose variations. To cope with this problem, a promising solution is to integrate the temporal…

This paper introduces a new modeling framework for the statistical analysis of point patterns on a manifold M_{d}, defined by a connected and compact two-point homogeneous space, including the special case of the sphere. The presented…

In this paper we propose a method that estimates the $SE(3)$ continuous trajectories (orientation and translation) of the dynamic rigid objects present in a scene, from multiple RGB-D views. Specifically, we fit the object trajectories to…

Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for…

Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint…

In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…

In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…

Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…