相关论文: A modified version of frozen percolation on the bi…
We investigate numerically and analytically the formation of the frozen core in critical random Boolean networks with biased functions. We demonstrate that a previously used efficient algorithm for obtaining the frozen core, which starts…
Observations and theory suggest that star clusters can form in a subvirial (cool) state and are highly substructured. Such initial conditions have been proposed to explain the level of mass segregation in clusters through dynamics, and have…
We investigate a population of primordial binaries during the initial stage of evolution of a star cluster. For our calculations we assume that equal mass stars form rapidly in a tidally truncated gas cloud, that $\sim10$\% of the stars are…
Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We define a modification of the Erdos-Renyi random graph process which can be regarded as the mean field frozen percolation process. We describe the behavior of the process using differential equations and investigate their solutions in…
In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $\gamma(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
Irreversible aggregation processes involving reactive and frozen clusters are investigated using the rate equation approach. In aggregation events, two clusters join irreversibly to form a larger cluster, and additionally, reactive clusters…
We study information aggregation in networks where agents make binary decisions (labeled incorrect or correct). Agents initially form independent private beliefs about the better decision, which is correct with probability $1/2+\delta$. The…
We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…
It is shown here that the percolation cluster that emerges from the percolation process on infinite perfect binary trees, is genuinely an encoding scheme for an infinite set of symbols. The average codeword length and the entropy of such an…
We analyze a simple model for growing tree networks and find that although it never percolates, there is an anomalously large cluster at finite size. We study the growth of both the maximal cluster and the cluster containing the original…
One class of random walks with infinite memory, so called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We…
We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with $\mathbb{Z}$, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
We consider the model of random trees introduced by Devroye (1999), the so-called random split trees. The model encompasses many important randomized algorithms and data structures. We then perform supercritical Bernoulli bond-percolation…
We show how to freeze distributed entanglement that has been created from the natural dynamics of spin chain systems. The technique that we propose simply requires single-qubit operations and isolates the entanglement in specific qubits at…