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Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from…

Video-based person re-identification aims to match pedestrians from video sequences across non-overlapping camera views. The key factor for video person re-identification is to effectively exploit both spatial and temporal clues from video…

Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…

Nodes movements play a significant role in disseminating messages in the sparse mobile ad-hoc network. In the network scenarios, where traditional end-to-end paths do not exist, mobility creates opportunities for nodes to connect and…

We address the problem of retrieving a specific moment from an untrimmed video by a query sentence. This is a challenging problem because a target moment may take place in relations to other temporal moments in the untrimmed video. Existing…

The real-time electronic dynamics on material surfaces is critically important to a variety of applications. However, their simulations have remained challenging for conventional methods such as the time-dependent density-functional theory…

The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…

We report on a data-driven investigation aimed at understanding the dynamics of message spreading in a real-world dynamical network of human proximity. We use data collected by means of a proximity-sensing network of wearable sensors that…

Network science has released its talents in social network analysis based on the information of static topologies. In reality social contacts are dynamic and evolve concurrently in time. Nowadays they can be recorded by ubiquitous…

In this short note, a topos - called the topos of the connectivity space - is associated with every such space.

Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar…

Temporal contexts among consecutive frames are far from being fully utilized in existing visual trackers. In this work, we present TCTrack, a comprehensive framework to fully exploit temporal contexts for aerial tracking. The temporal…

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…

Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on…

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…