scholarly journals Finitely forcible graphons with an almost arbitrary structure

2020 ◽  
Author(s):  
Jonathan Noel ◽  
◽  
Daniel Kral ◽  
Laszlo Miklos Lovasz ◽  
Jakub Sosnovec
Keyword(s):  
Random Graph ◽  
Basic Result ◽  
Arbitrary Structure

A basic result from the theory of quasirandom graphs, due to Andrew Thomason, is that if is a graph with vertices and density , and if the number of 4-cycles in is approximately , then resembles a random graph of the same density. In particular, between any two sets and of vertices the number of edges is approximately . (Here, “approximately” means "to within a small fraction of , so the statement is non-trivial only for sets and that are not too small.)

Legal Protection Of Heirs Testamenter To Testament Agreement Which Not Registered (Case Study Testamenter Without Heirs)

Jurnal Akta ◽  
2018 ◽  
Vol 5 (2) ◽  
pp. 421
Author(s):  
Amalia Putri Prima Erdian ◽  
Arief Cholil
Keyword(s):  
Basic Result ◽  
Legal Protection ◽  
Public Official ◽  
The Will ◽  
The Creation ◽  
Registered Case

Law of inheritance only happens because the person died. In BW there are two ways to get wealth, that is: as heirs according to the provisions of law and as a person appointed in the will. What is meant by the will itself according to Article 875 BW is an agreement that make statements about what he wished someone would happen after he died, and that by her to pull back. In general, people make a will before a Public Notary. According to article 1 paragraph 1 of Act No. 2 of 2014 concerning On Notary (now referred to UUJN). Notary is a public official who is authorized to make authentic agreements and other authorities referred to in the Act, where each testament must be shaped agreement in order to obtain certainty law as an authentic agreement binding. With the creation of the will meant that the parties can understand and be able to know the basic result of the offense can be arranged so that the interests of the concerned receive proper protection as known by the Notary.Keywords: Inheritance; Heir; Testament; Authentic Agreement

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

scholarly journals A Note on the Majority Dynamics in Inhomogeneous Random Graphs

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graph ◽  
Initial State ◽  
Time Step ◽  
Dynamic Monopoly ◽  
Inhomogeneous Random Graphs ◽  
Assignment Probability ◽  
Edge Probability ◽  
Consensus Reaching Process ◽  
Consensus Reaching ◽  
Inhomogeneous Random Graph

AbstractIn this note, we study discrete time majority dynamics over an inhomogeneous random graph G obtained by including each edge e in the complete graph $$K_n$$ K n independently with probability $$p_n(e)$$ p n ( e ) . Each vertex is independently assigned an initial state $$+1$$ + 1 (with probability $$p_+$$ p + ) or $$-1$$ - 1 (with probability $$1-p_+$$ 1 - p + ), updated at each time step following the majority of its neighbors’ states. Under some regularity and density conditions of the edge probability sequence, if $$p_+$$ p + is smaller than a threshold, then G will display a unanimous state $$-1$$ - 1 asymptotically almost surely, meaning that the probability of reaching consensus tends to one as $$n\rightarrow \infty $$ n → ∞ . The consensus reaching process has a clear difference in terms of the initial state assignment probability: In a dense random graph $$p_+$$ p + can be near a half, while in a sparse random graph $$p_+$$ p + has to be vanishing. The size of a dynamic monopoly in G is also discussed.

Mixed failure-driven and shock-driven mission aborts in heterogeneous systems with arbitrary structure

2021 ◽  
Vol 212 ◽  
pp. 107581
Author(s):  
Gregory Levitin ◽  
Liudong Xing ◽  
Yanping Xiang ◽  
Yuanshun Dai
Keyword(s):  
Heterogeneous Systems ◽  
Arbitrary Structure
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