相关论文: Jacobi Set Simplification for Tracking Topological…

We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…

A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal matrix with invertible blocks on the off-diagonals. Averaging over boundary conditions leads to explicit formulas for the averaged spectral measure which can…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

This report proposes an improved method for the Tracking Any Point (TAP) task, which tracks any physical surface through a video. Several existing approaches have explored the TAP by considering the temporal relationships to obtain smooth…

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

In this paper, we propose a novel trajectory learning method that exploits motion trajectories on topological map using recurrent neural network for temporally consistent geolocalization of object. Inspired by human's ability to both be…

This paper proposes a method for automatically monitoring and analyzing the evolution of complex geographic objects. The objects are modeled as a spatiotemporal graph, which separates filiation relations, spatial relations, and…

The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathematics, and in particular in topological data analysis, where…

Feature extraction is a critical technology to realize the automatic transmission of feature information throughout product life cycles. As CAD models primarily capture the 3D geometry of products, feature extraction heavily relies on…

Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

We consider the classical sensor scheduling problem for linear systems where only one sensor is activated at each time. We show that the sensor scheduling problem has a close relation to the sensor design problem and the solution of a…

Batch effects in high-dimensional Cytometry by Time-of-Flight (CyTOF) data pose a challenge for comparative analysis across different experimental conditions or time points. Traditional batch normalization methods may fail to preserve the…

We study how topological defects manifest themselves in the equal-time two-point field correlator. We consider a scalar field with Z_2 symmetry in 1, 2 and 3 spatial dimensions, allowing for kinks, domain lines and domain walls,…

We consider a class of Jacobi matrices with unbounded coefficients. This class is known to exhibit a first-order phase transition in the sense that, as a parameter is varied, one has purely discrete spectrum below the transition point and…

This paper addresses optimal feedback stabilizing control for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations, affected by state and process noise. Instead of directly stabilizing the uncertain system, we…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

In this paper we devise a statistical method for tracking and modeling change-points on the dependence structure of multivariate extremes. The methods are motivated by and illustrated on a case study on crypto-assets.