Related papers: Time-Varying Spaces and Mobile Sensor Networks

One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…

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…

Axial vectors, such as current or magnetization, are commonly used order parameters in time-reversal symmetry breaking systems. These vectors also break isotropy in three dimensional systems, lowering the spatial symmetry. We demonstrate…

In this paper we consider a robot patrolling problem in which events arrive randomly over time at the vertices of a graph. When an event arrives it remains active for a random amount of time. If that time active exceeds a certain threshold,…

We propose categories of $1$-dimensional and multi-dimensional quantum walks. In the categories, an object is a quantum walk, and a morphism is an intertwining operator between two quantum walks. The new framework enables us to discuss…

Robust state estimation in coupled dynamical systems depends critically not only on sensor quality but on the structural alignment between observation channels and the system's intrinsic dynamics. This paper develops a rigorous framework…

This paper aims to unify spatial dependency and temporal dependency in a non-Euclidean space while capturing the inner spatial-temporal dependencies for traffic data. For spatial-temporal attribute entities with topological structure, the…

The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can…

The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this "deterministic random walk" covers all…

We investigate crossing path probabilities for two agents that move randomly in a bounded region of the plane or on a sphere (denoted $R$). At each discrete time-step the agents move, independently, fixed distances $d_1$ and $d_2$ at angles…

Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastucture, road networks, flight connections, brain functional networks and social networks. The effect of…

Multi-photon quantum walks in integrated optics are an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light…

We study covert communications over binary-input discrete memoryless alarm two-way channels, in which two users interact through a two-way channel and attempt to hide the presence of their communication from an eavesdropping receiver. The…

Using time as an additional design parameter in electromagnetism, photonics, and wave physics is attracting considerable research interest, motivated by the possibility to explore physical phenomena and engineering opportunities beyond the…

Photonic time crystals are electromagnetic media with periodically time-varying parameters, enabling momentum band gaps, parametric amplification, and frequency conversion beyond what is possible in time-invariant systems. So far, they have…

The dynamical discrete web is a system of one-dimensional coalescing random walks that evolves in an extra dynamical time parameter. At any deterministic dynamical time, the paths behave as coalescing simple symmetric random walks. This…

This work is motivated by an original dataset of reported mumps cases across nine regions of England, and focuses on the modeling of temporal dynamics and time-varying dependency patterns between the observed time series. The goal is to…

Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…

With the advent of advanced 4G/5G mobile networks, mobile phone data collected by operators now includes detailed, service-specific traffic information with high spatio-temporal resolution. In this paper, we leverage this type of data to…

This paper considers the distributed sampled-data control problem of a group of mobile robots connected via distance-induced proximity networks. A dwell time is assumed in order to avoid chattering in the neighbor relations that may be…