相关论文: Jacobi Set Simplification for Tracking Topological…

As an important and challenging problem in computer vision and graphics, keypoint-based object tracking is typically formulated in a spatio-temporal statistical learning framework. However, most existing keypoint trackers are incapable of…

Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time.…

Motivated by the Hamilton$-$Jacobi approach of fields with constraints, we analyse the classical structure of three different constrained field systems: (i) the scalar field coupled to two flavors of fermions through Yukawa couplings (ii)…

We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…

Temporal set prediction involves forecasting the elements that will appear in the next set, given a sequence of prior sets, each containing a variable number of elements. Existing methods often rely on intricate architectures with…

Maintaining stable and accurate localization during fast motion or on rough terrain remains highly challenging for mobile robots with onboard resources. Currently, multi-sensor fusion methods based on continuous-time representation offer a…

Identifying systematic patterns in seismicity that precede large earthquakes remains a central challenge in statistical seismology. In this work, we present a methodological framework for detecting spatiotemporal anomalies in seismicity…

In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems,…

The computational efficiency and rapid convergence of fast Fourier transform (FFT)-based solvers render them a powerful numerical tool for periodic cell problems in multiscale modeling. On regular grids, they tend to outperform traditional…

This paper addresses the ubiquity of remarkable measures on graphs, and their applications. In many queueing systems, it is necessary to take into account the compatibility constraints between users, or between supply and demands, and so…

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data we need to account for relations among both time…

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the…

We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in…

We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase…

We study Jacobi matrices on star-like graphs, which are graphs that are given by the pasting of a finite number of half-lines to a compact graph. Specifically, we extend subordinacy theory to this type of graphs, that is, we find a…

It is quite common that the structure of a time series changes abruptly. Identifying these change points and describing the model structure in the segments between these change points is of interest. In this paper, time series data is…

We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess…

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely…

We study the properties and asymptotics of the Jacobi matrices associated with equilibrium measures of the weakly equilibrium Cantor sets. These family of Cantor sets were defined and different aspects of orthogonal polynomials on them were…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…