Related papers: Target-searching on the percolation
We use deep-learning strategies to study the 2D percolation model on a square lattice. We employ standard image recognition tools with a multi-layered convolutional neural network. We test how well these strategies can characterise…
We present a coupled decreasing sequence of random walks on $ \mathbb Z $ that dominates the edge process of oriented-bond percolation in two dimensions. Using the concept of "random walk in a strip ", we construct an algorithm that…
We determine thresholds $p_c$ for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their complex combinations. There are 31 distinct…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Adaptive sampling and planning in robotic environmental monitoring are challenging when the target environmental process varies over space and time. The underlying environmental dynamics require the planning module to integrate future…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
In this work we develop clustering techniques for the Bearing Only Target Localization (BOTL) problem. Our scenario has a receiver move along some path, generating bearing estimates on some interval. Multiple emitting targets exist in the…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
Adversarial search of a network for an immobile Hider (or target) was introduced and solved for rooted trees by Gal (1979). In this zero-sum game, a Hider picks a point to hide on the tree and a Searcher picks a unit speed trajectory…
We consider the cluster and backbone mass distributions between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold $p_c$. We…
A kinetic Monte Carlo method was used to simulate the diffusion of reptating polymer chains across the interface. A time-resolved fluorescence technique conjunction with direct energy transfer method was used to measure the extend of…
To work in unknown outdoor environments, autonomous sampling machines need the ability to target samples despite limited visibility and robotic arm reach distance. We design a heuristic guided search method to speed up the search process…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte-Carlo simulations with the (local) heat-bath method. We find qualitatively…
In cluster tomography, we propose measuring the number of clusters $N$ intersected by a line segment of length $\ell$ across a finite sample. As expected, the leading order of $N(\ell)$ scales as $a\ell$, where $a$ depends on microscopic…
Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal…
We present a model of speech perception which takes into account effects of correlations between sounds. Words in this model correspond to the attractors of a suitably chosen descent dynamics. The resulting lexicon is rich in short words,…
We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice…
We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this…
We study the capture of a diffusing "lamb" by diffusing "lions" in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics…