scholarly journals A sharp threshold for bootstrap percolation in a random hypergraph

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Natasha Morrison ◽  
Jonathan A. Noel
Keyword(s):  
Bootstrap Percolation ◽  
Sharp Threshold ◽  
Random Hypergraph

scholarly journals The sharp threshold for bootstrap percolation in all dimensions

2012 ◽  
Vol 364 (5) ◽  
pp. 2667-2701 ◽  
Author(s):  
József Balogh ◽  
Béla Bollobás ◽  
Hugo Duminil-Copin ◽  
Robert Morris
Keyword(s):  
Bootstrap Percolation ◽  
Sharp Threshold

scholarly journals A Sharp Threshold for a Modified Bootstrap Percolation with Recovery

2014 ◽  
Vol 157 (3) ◽  
pp. 531-570 ◽  
Author(s):  
Tom Coker ◽  
Karen Gunderson
Keyword(s):  
Bootstrap Percolation ◽  
Sharp Threshold

scholarly journals On Rainbow Hamilton Cycles in Random Hypergraphs

10.37236/7274 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Andrzej Dudek ◽  
Sean English ◽  
Alan Frieze
Keyword(s):  
Hamilton Cycle ◽  
Uniform Hypergraph ◽  
Hamilton Cycles ◽  
Sharp Threshold ◽  
Vertex Set ◽  
Different Color ◽  
Random Hypergraph ◽  
Random Hypergraphs

Let $H_{n,p,r}^{(k)}$ denote a randomly colored random hypergraph, constructed on the vertex set $[n]$ by taking each $k$-tuple independently with probability $p$, and then independently coloring it with a random color from the set $[r]$. Let $H$ be a $k$-uniform hypergraph of order $n$. An $\ell$-Hamilton cycle is a spanning subhypergraph $C$ of $H$ with $n/(k-\ell)$ edges and such that for some cyclic ordering of the vertices each edge of $C$ consists of $k$ consecutive vertices and every pair of adjacent edges in $C$ intersects in precisely $\ell$ vertices.In this note we study the existence of rainbow $\ell$-Hamilton cycles (that is every edge receives a different color) in $H_{n,p,r}^{(k)}$. We mainly focus on the most restrictive case when $r = n/(k-\ell)$. In particular, we show that for the so called tight Hamilton cycles ($\ell=k-1$) $p = e^2/n$ is the sharp threshold for the existence of a rainbow tight Hamilton cycle in $H_{n,p,n}^{(k)}$ for each $k\ge 4$.

Transport through bootstrap percolation clusters

1991 ◽  
Vol 1 (5) ◽  
pp. 685-692 ◽  
Author(s):  
Muhammad Sahimi ◽  
Tane S. Ray
Keyword(s):  
Bootstrap Percolation ◽  
Percolation Clusters

scholarly journals Abelian cascade dynamics in bootstrap percolation

1998 ◽  
Vol 261 (3-4) ◽  
pp. 351-358 ◽  
Author(s):  
S.S. Manna
Keyword(s):  
Bootstrap Percolation

scholarly journals Semi-Supervised Classification via Hypergraph Convolutional Extreme Learning Machine

2021 ◽  
Vol 11 (9) ◽  
pp. 3867
Author(s):  
Zhewei Liu ◽  
Zijia Zhang ◽  
Yaoming Cai ◽  
Yilin Miao ◽  
Zhikun Chen
Keyword(s):  
Extreme Learning Machine ◽  
Supervised Classification ◽  
Structured Data ◽  
Model Complex ◽  
Euclidean Domain ◽  
Noise Data ◽  
Data Points ◽  
Learning Machine ◽  
Random Hypergraph ◽  
Special Case

Extreme Learning Machine (ELM) is characterized by simplicity, generalization ability, and computational efficiency. However, previous ELMs fail to consider the inherent high-order relationship among data points, resulting in being powerless on structured data and poor robustness on noise data. This paper presents a novel semi-supervised ELM, termed Hypergraph Convolutional ELM (HGCELM), based on using hypergraph convolution to extend ELM into the non-Euclidean domain. The method inherits all the advantages from ELM, and consists of a random hypergraph convolutional layer followed by a hypergraph convolutional regression layer, enabling it to model complex intraclass variations. We show that the traditional ELM is a special case of the HGCELM model in the regular Euclidean domain. Extensive experimental results show that HGCELM remarkably outperforms eight competitive methods on 26 classification benchmarks.

On the s-Colorful Number of a Random Hypergraph

2021 ◽  
Author(s):  
D. A. Shabanov
Keyword(s):  
Random Hypergraph

scholarly journals Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hui Zhou ◽  
Jehad Alzabut ◽  
Shahram Rezapour ◽  
Mohammad Esmael Samei
Keyword(s):  
Differential Inequality ◽  
Almost Periodic Solution ◽  
Rocky Intertidal ◽  
Uniform Persistence ◽  
Almost Periodic ◽  
Patch Occupancy ◽  
Sharp Threshold ◽  
Intertidal Community ◽  
Patch Occupancy Model ◽  
Inequality Techniques

Abstract In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes.

A multigroup model for cholera dynamics and control

2015 ◽  
Vol 09 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Drew Posny ◽  
Chairat Modnak ◽  
Jin Wang
Keyword(s):  
Reproduction Number ◽  
Vaccination Strategy ◽  
Sharp Threshold ◽  
Indirect Transmission ◽  
Dynamics And Control ◽  
Simulation Results ◽  
Transmission Pathways ◽  
And Control ◽  
Control Study ◽  
The Basic Reproduction Number

We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that the basic reproduction number R0 remains a sharp threshold for cholera dynamics in multigroup settings. We verify the analysis by numerical simulation results. We also perform an optimal control study to explore optimal vaccination strategy for cholera outbreaks.

Comparison of bootstrap percolation models

1989 ◽  
Vol 22 (7) ◽  
pp. L297-L301 ◽  
Author(s):  
J Adler ◽  
D Stauffer ◽  
A Aharony
Keyword(s):  
Bootstrap Percolation
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