Related papers: Time-Varying Spaces and Mobile Sensor Networks
Suppose that ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid…
Given a compact manifold $X$ with boundary and a submersion $f : X \rightarrow Y$ whose restriction to the boundary of $X$ has isolated critical points with distinct critical values and where $Y$ is $[0,1]$ or $S^1$, the connected…
Suppose one wants to monitor a domain with sensors, each sensing a small ball-shaped region, but the domain is hazardous enough that one cannot control the placement of the sensors. A prohibitively large number of randomly placed sensors…
The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We use the Bousfield-Kan spectral sequence for homotopy inverse…
In this paper we study the dynamic aspects of the coverage of a mobile sensor network resulting from continuous movement of sensors. As sensors move around, initially uncovered locations are likely to be covered at a later time. A larger…
This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
Time-varying graph signals are alternative representation of multivariate (or multichannel) signals in which a single time-series is associated with each of the nodes or vertex of a graph. Aided by the graph-theoretic tools, time-varying…
In this paper, we study asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented only based on the state information at some…
Correlation of interference affects spatio-temporal aspects of various wireless mobile systems, such as retransmission, multiple antennas and cooperative relaying. In this paper, we study the spatial and temporal correlation of interference…
We study the role that both vacuum fluctuations and vacuum entanglement of a scalar field play in identifying the spacetime topology, which is not prescribed from first principles---neither in general relativity or quantum gravity. We…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological…
Time-variant systems have recently garnered considerable attention due to their unique potentials in manipulating electromagnetic waves. Here, a novel class of topological spacetime crystals is introduced, with a traveling-wave modulation…
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the…
We consider networks of noisy degraded wiretap channels in the presence of an eavesdropper. For the case where the eavesdropper can wiretap at most one channel at a time, we show that the secrecy capacity region, for a broad class of…
Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with…
Recently spatial as well as temporal variations of the fine structure constant alpha have been reported. We show that a "runaway domain wall", which arises for the scalar field potential without minima, can account for such variations…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…