scholarly journals A phase transition in the evolution of bootstrap percolation processes on preferential attachment graphs

2017 ◽  
Vol 52 (3) ◽  
pp. 379-418 ◽  
Author(s):  
Mohammed Amin Abdullah ◽  
Nikolaos Fountoulakis
Keyword(s):  
Phase Transition ◽  
Preferential Attachment ◽  
Bootstrap Percolation ◽  
Percolation Processes

scholarly journals Percolation phase transition in weight-dependent random connection models

2021 ◽  
Vol 53 (4) ◽  
pp. 1090-1114
Author(s):  
Peter Gracar ◽  
Lukas Lüchtrath ◽  
Peter Mörters
Keyword(s):  
Phase Transition ◽  
Poisson Process ◽  
Random Graphs ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Dimensional Space ◽  
Geometric Model ◽  
Scale Free ◽  
Power Law Exponent

AbstractWe investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.

scholarly journals Preferential Attachment with Location-Based Choice: Degree Distribution in the Noncondensation Phase

2021 ◽  
Vol 184 (1) ◽  
Author(s):  
Arne Grauer ◽  
Lukas Lüchtrath ◽  
Mark Yarrow
Keyword(s):  
Phase Transition ◽  
Power Law ◽  
Degree Distribution ◽  
Maximum Degree ◽  
Preferential Attachment ◽  
Critical Value ◽  
Time Step ◽  
Power Law Exponent ◽  
Attachment Model ◽  
Sampling Probability

AbstractWe consider the preferential attachment model with location-based choice introduced by Haslegrave et al. (Random Struct Algorithms 56(3):775–795, 2020) as a model in which condensation phenomena can occur. In this model, each vertex carries an independent and uniformly distributed location. Starting from an initial tree, the model evolves in discrete time. At every time step, a new vertex is added to the tree by selecting r candidate vertices from the graph with replacement according to a sampling probability proportional to these vertices’ degrees. The new vertex then connects to one of the candidates according to a given probability associated to the ranking of their locations. In this paper, we introduce a function that describes the phase transition when condensation can occur. Considering the noncondensation phase, we use stochastic approximation methods to investigate bounds for the (asymptotic) proportion of vertices inside a given interval of a given maximum degree. We use these bounds to observe a power law for the asymptotic degree distribution described by the aforementioned function. Hence, this function fully characterises the properties we are interested in. The power law exponent takes the critical value one at the phase transition between the condensation–noncondensation phase.

scholarly journals Особенности влияния состава и кристаллической структуры на поведение электрофизических свойств сплавов системы Ni-=SUB=-(1-x)-=/SUB=-W-=SUB=-x-=/SUB=- при низких температурах

2018 ◽  
Vol 60 (10) ◽  
pp. 1888
Author(s):  
В.В. Деревянко ◽  
М.С. Сунгуров ◽  
Т.В. Сухарeва ◽  
В.А. Финкель ◽  
Ю.Н. Шахов
Keyword(s):  
Phase Transition ◽  
The Other ◽  
Two Phase ◽  
Magnetic Structures ◽  
Concentration Dependences ◽  
Temperature Dependences ◽  
Chemical And Phase Compositions ◽  
The One ◽  
Percolation Processes ◽  
Bcc Phase

AbstractThe problem of establishing the correlation between, on the one hand, the chemical and phase compositions of Ni_1– x W_ x alloys (0 ≤ x ≤ 0.5) and, on the other hand, the character of the temperature dependences of the electrical resistivity, is considered. Based on the experimental ρ( T ) curves, the concentration dependences of are reconstructed in the wide temperature range (50 K ≤ T ≤ 273 K). The ρ( x ) curves have features related to a change in the crystal structures of the alloys (concentration fcc–bcc phase transition), their magnetic structures and percolation processes occurring in the two-phase fcc + bcc medium.

scholarly journals ANDRZEJ PȨKALSKI NETWORKS OF SCIENTIFIC INTERESTS WITH INTERNAL DEGREES OF FREEDOM THROUGH SELF-CITATION ANALYSIS

2008 ◽  
Vol 19 (03) ◽  
pp. 371-384 ◽  
Author(s):  
M. AUSLOOS ◽  
R. LAMBIOTTE ◽  
A. SCHARNHORST ◽  
I. HELLSTEN
Keyword(s):  
Degrees Of Freedom ◽  
Network Formation ◽  
Preferential Attachment ◽  
Citation Network ◽  
Research Topics ◽  
Internal Shock ◽  
Field Mobility ◽  
Shock Resistance ◽  
Percolation Processes ◽  
Internal Degrees Of Freedom

Old and recent theoretical works by Andrzej Pȩkalski (APE) are recalled as possible sources of interest for describing network formation and clustering in complex (scientific) communities, through self-organization and percolation processes. Emphasis is placed on APE self-citation network over four decades. The method is that used for detecting scientists' field mobility by focusing on author's self-citation, co-authorships and article topics networks as in Refs. 1 and 2. It is shown that APE's self-citation patterns reveal important information on APE interest for research topics over time as well as APE engagement on different scientific topics and in different networks of collaboration. Its interesting complexity results from "degrees of freedom" and external fields leading to so called internal shock resistance. It is found that APE network of scientific interests belongs to independent clusters and occurs through rare or drastic events as in irreversible "preferential attachment processes", similar to those found in usual mechanics and thermodynamics phase transitions.

scholarly journals Multiple hybrid phase transition: Bootstrap percolation on complex networks with communities

2014 ◽  
Vol 107 (4) ◽  
pp. 48001 ◽  
Author(s):  
Chong Wu ◽  
Shenggong Ji ◽  
Rui Zhang ◽  
Liujun Chen ◽  
Jiawei Chen ◽  
...  
Keyword(s):  
Phase Transition ◽  
Complex Networks ◽  
Bootstrap Percolation
Sign in / Sign up

Export Citation Format

Share Document