Related papers: Connectedness, Continuity, and Proximities in Temp…

The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…

Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…

Temporal network analysis and time evolution of network characteristics are powerful tools in describing the changing topology of dynamic networks. This paper uses such approaches to better visualize and provide analytical measures for the…

The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.

Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…

Online contextual reasoning and association across consecutive video frames are critical to perceive instances in visual tracking. However, most current top-performing trackers persistently lean on sparse temporal relationships between…

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…

Most work on temporal action detection is formulated as an offline problem, in which the start and end times of actions are determined after the entire video is fully observed. However, important real-time applications including…

Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…

In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…

Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with…

It has recently become possible to record detailed social interactions in large social systems with high resolution. As we study these datasets, human social interactions display patterns that emerge at multiple time scales, from minutes to…

Networks evolve continuously over time with the addition, deletion, and changing of links and nodes. Such temporal networks (or edge streams) consist of a sequence of timestamped edges and are seemingly ubiquitous. Despite the importance of…

We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The results are obtained by constructing and studying the…

By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…

Many real-world datasets -- from an artist's body of work to a person's social media history -- exhibit meaningful semantic changes over time that are difficult to capture with existing dimensionality reduction methods. To address this gap,…

Understanding the structures why links are formed is an important and prominent research topic. In this paper, we therefore consider the link prediction problem in face-to-face contact networks, and analyze the predictability of new and…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

We consider the problem of localizing a spatio-temporal tube in a video corresponding to a given text query. This is a challenging task that requires the joint and efficient modeling of temporal, spatial and multi-modal interactions. To…

Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…