相关论文: Jacobi Set Simplification for Tracking Topological…

Biadjoint scalar field theories appear in the study of scattering amplitudes and classical solutions in gauge, gravity and related theories. In this paper, we present new exact solutions of biadjoint scalar field theory, showing that…

Existing tools for bifurcation detection from signals of dynamical systems typically are either limited to a special class of systems, or they require carefully chosen input parameters, and significant expertise to interpret the results.…

We propose a two-stage approach Spec PC-CP to identify change points in multivariate time series. In the first stage, we obtain a low-dimensional summary of the high-dimensional time series by Spectral Principal Component Analysis…

There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…

Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…

Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…

Fast appearance variations and the distractions of similar objects are two of the most challenging problems in visual object tracking. Unlike many existing trackers that focus on modeling only the target, in this work, we consider the…

Graphs are commonly used to represent objects, such as images and text, for pattern classification. In a dynamic world, an object may continuously evolve over time, and so does the graph extracted from the underlying object. These changes…

The bicategory of parameterized spectra has a remarkably rich structure. In particular, it is possible to take traces in this bicategory, which give classical invariants that count fixed points. We can also take equivariant traces, which…

Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such…

Visual tracking has made significant improvements in the past few decades. Most existing state-of-the-art trackers 1) merely aim for performance in ideal conditions while overlooking the real-world conditions; 2) adopt the…

This paper introduces a novel technique to track structures in time varying graphs. The method uses a maximum a posteriori approach for adjusting a three-dimensional co-clustering of the source vertices, the destination vertices and the…

One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…

Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…

The constrained filed system, the scalar field coupled to two flavours of fermions through Yukawa couplings, is treated by using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many…

Searching topological similarity between a pair of shapes or data is an important problem in data analysis and visualization. The problem of computing similarity measures using scalar topology has been studied extensively and proven useful…

We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…

We introduce time-varying extremum graph (TVEG), a topological structure to support visualization and analysis of a time-varying scalar field. The extremum graph is a substructure of the Morse-Smale complex. It captures the adjacency…

In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a…

The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…