The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence

Local Weak Convergence Based Analysis of a New Graph Model

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton) ◽

10.1109/allerton.2018.8635966 ◽

2018 ◽

Author(s):

M. Moharrami ◽

V. Subramanian ◽

M. Liu ◽

R. Sundaresan

Keyword(s):

Weak Convergence ◽

Graph Model ◽

Local Weak Convergence

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Local weak convergence for PageRank

The Annals of Applied Probability ◽

10.1214/19-aap1494 ◽

2020 ◽

Vol 30 (1) ◽

pp. 40-79

Author(s):

Alessandro Garavaglia ◽

Remco van der Hofstad ◽

Nelly Litvak

Keyword(s):

Weak Convergence ◽

Local Weak Convergence

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Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method

Random Structures and Algorithms ◽

10.1002/rsa.20072 ◽

2005 ◽

Vol 28 (1) ◽

pp. 76-106 ◽

Cited By ~ 24

Author(s):

David Gamarnik ◽

Tomasz Nowicki ◽

Grzegorz Swirszcz

Keyword(s):

Weak Convergence ◽

Random Graphs ◽

Independent Sets ◽

Exact Results ◽

Maximum Weight ◽

Convergence Method ◽

Local Weak Convergence ◽

Weak Convergence Method

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Random intersection graphs with communities

Advances in Applied Probability ◽

10.1017/apr.2021.12 ◽

2021 ◽

Vol 53 (4) ◽

pp. 1061-1089

Author(s):

Remco van der Hofstad ◽

Júlia Komjáthy ◽

Viktória Vadon

Keyword(s):

Weak Convergence ◽

Internal Structure ◽

Degree Distribution ◽

Clustering Coefficient ◽

Intersection Graphs ◽

Structure Of Communities ◽

Local Clustering ◽

Model Networks ◽

Local Weak Convergence ◽

Local Clustering Coefficient

AbstractRandom intersection graphs model networks with communities, assuming an underlying bipartite structure of communities and individuals, where these communities may overlap. We generalize the model, allowing for arbitrary community structures within the communities. In our new model, communities may overlap, and they have their own internal structure described by arbitrary finite community graphs. Our model turns out to be tractable. We analyze the overlapping structure of the communities, show local weak convergence (including convergence of subgraph counts), and derive the asymptotic degree distribution and the local clustering coefficient.

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Accessibility percolation on random rooted labeled trees

Journal of Applied Probability ◽

10.1017/jpr.2019.29 ◽

2019 ◽

Vol 56 (2) ◽

pp. 533-545

Author(s):

Zhishui Hu ◽

Zheng Li ◽

Qunqiang Feng

Keyword(s):

Weak Convergence ◽

Explicit Form ◽

Random Vector ◽

Generating Function ◽

Probability Generating Function ◽

Percolation Model ◽

Asymptotic Distributions ◽

Labeled Trees ◽

Local Weak Convergence ◽

Labeled Tree

AbstractThe accessibility percolation model is investigated on random rooted labeled trees. More precisely, the number of accessible leaves (i.e. increasing paths) Zn and the number of accessible vertices Cn in a random rooted labeled tree of size n are jointly considered in this work. As n → ∞, we prove that (Zn, Cn) converges in distribution to a random vector whose probability generating function is given in an explicit form. In particular, we obtain that the asymptotic distributions of Zn + 1 and Cn are geometric distributions with parameters e/(1 + e) and 1/e, respectively. Much of our analysis is performed in the context of local weak convergence of random rooted labeled trees.

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Double hashing thresholds via local weak convergence

2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton) ◽

10.1109/allerton.2013.6736515 ◽

2013 ◽

Author(s):

M. Leconte

Keyword(s):

Weak Convergence ◽

Local Weak Convergence

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Disappearance Voltage Determinations Using a Convergent Beam

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100064979 ◽

1971 ◽

Vol 29 ◽

pp. 184-185

Author(s):

W. L. Bell

Keyword(s):

Second Order ◽

Objective Method ◽

Uniform Thickness ◽

Rocking Curve ◽

Crystal Perfection ◽

Kikuchi Line ◽

Central Maximum ◽

Diffraction Patterns ◽

Convergent Beam ◽

Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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