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Product Measure Approximation of Symmetric Graph Properties
[article]

2015
*
arXiv
*
pre-print

With this in mind, we pursue the following question: What are general sufficient conditions for the uniform

arXiv:1502.07787v1
fatcat:itw5tacwdfg6xpfbdgt5atusle
*measure*on a set*of**graphs*S ⊆G_n to be*approximable*by a*product**measure*? ... Let G_n be the set*of*all*graphs*on n vertices and let S be an arbitrary subset*of*G_n, e.g., the set*of**graphs*with m edges. ... On one hand was the desire to explore the extent to which*symmetric*sets (*properties*) can be studied via*product**measure**approximations*(instead*of*assuming*product*form and studying*properties**of*the ...##
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Symmetric Graph Properties Have Independent Edges
[chapter]

2015
*
Lecture Notes in Computer Science
*

With this in mind, we pursue the following question: What are general sufficient conditions for the uniform

doi:10.1007/978-3-662-47666-6_37
fatcat:uqf5alercfahjamg2z45olnkau
*measure*on a set*of**graphs*S ⊆ Gn to be well-*approximable*by a*product**measure*on the set*of*... Let Gn be the set*of*all*graphs*on n vertices and let S be an arbitrary subset*of*Gn, e.g., the set*of*all*graphs*with m edges. ... Conditional on the edge-profile, we can couple the generation*of*edges in different parts independently, in each part the coupling being identical to that between G(n, m) and G(n, p). ...##
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A New Algorithm to Compute Low T-Transitive Approximation of a Fuzzy Relation Preserving Symmetry. Comparisons with the T-Transitive Closure
[chapter]

2005
*
Lecture Notes in Computer Science
*

It is given a new algorithm to compute a lower T-transitive

doi:10.1007/11518655_49
fatcat:6uulvhsvinchxgbffj66ugbrji
*approximation**of*a fuzzy relation that preserves symmetry. ... Average distances*of*the fuzzy relation with the Ttransitive closure are similar than the average distances with the low T-transitive*approximation*. ... Conclusions The T-transitivization algorithm that keeps symmetry, applies to reflexive and*symmetric*fuzzy relations, computes T-transitive low*approximations*with similar distances than the T-transitive ...##
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Inapproximability of actions and Kazhdan's property (T)
[article]

2019
*
arXiv
*
pre-print

We construct p.m.p. group actions that are not local-global limits

arXiv:1901.03963v2
fatcat:hgrojecj7zhtdjxfkhcknqem3i
*of*sequences*of*finite*graphs*. Moreover, they do not weakly contain any sequence*of*finite labeled*graphs*. ... Our methods are based on the study*of*almost automorphisms*of*sofic*approximations*: We show that the set*of*epsilon-automorphisms*of*a sufficiently good sofic*approximation**of*a Kazhdan group by expanders ... Acknowledgments The work*of*the authors has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Consolidator Grant No. 681207 ...##
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A Kernel-Based Framework for Learning Graded Relations From Data

2012
*
IEEE transactions on fuzzy systems
*

It extends existing approaches because both crisp and graded relations are considered, and it unifies existing approaches because different types

doi:10.1109/tfuzz.2012.2194151
fatcat:k5baor5zxzhpbizbusah3kzfze
*of*graded relations can be modeled, including*symmetric*... Driven by a large number*of*potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting*of*inferring relations between pairs*of*data objects ... and positive definiteness or transitivity*properties*for similarity*measures*. ...##
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Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

2018
*
Entropy
*

We show that

doi:10.3390/e20070534
pmid:33265623
fatcat:pmg65kxoabaqbadiarbiwzpr3m
*approximations*to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric,*symmetric*and topological*properties**of*mathematical ... We review, study and apply a method for*approximating*the algorithmic complexity (also known as Kolmogorov–Chaitin complexity)*of**graphs*and networks based on the concept*of*Algorithmic Probability (AP ... An essential ingredient for a complexity*measure*is that it integrates all its*properties*, something that only a noncomputable*approximating**measure*such as CTM/BDM can achieve. ...##
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Effective Resistance Preserving Directed Graph Symmetrization
[article]

2019
*
arXiv
*
pre-print

It is shown that the preservation

arXiv:1802.09829v2
fatcat:4x6w47usyrhc3m36ywoqf4xena
*of*this metric allows for interpretation*of*algebraic and spectral*properties**of*the*symmetrized**graph*in the context*of*the directed*graph*, due to the relationship between ... Additionally, Lyapunov theory is used to demonstrate that the Laplacian matrix*of*a directed*graph*can be decomposed into the*product**of*a projection matrix, a skew*symmetric*matrix, and the Laplacian ... Moreover, it is shown that the Laplacian matrix*of*a directed*graph*can be decomposed into the*product**of*a projection matrix, a skew*symmetric*matrix, and the Laplacian matrix*of*the*symmetrized**graph*...##
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Approximate reflectional symmetries of fuzzy objects with an application in model-based object recognition

2004
*
Fuzzy sets and systems (Print)
*

The choice

doi:10.1016/j.fss.2003.07.003
fatcat:qylaeuftxja7zpc7hu4lg3ax2e
*of*an appropriate*measure**of*comparison is based on the desired*properties**of*the symmetry*measure*. Then, an algorithm for computing the symmetry plane*of*fuzzy objects is proposed. ...*Approximate*reflectional symmetries*of*fuzzy objects with an application in model-based object recognition. Abstract This paper is devoted to the study*of*reflectional symmetries*of*fuzzy objects. ... One important*property**of*the symmetry attribute s(a, b) is that it will be zero for most pairs*of*regions which are not*symmetrical*, and non-zero only for a small group*of**approximately**symmetrical*pairs ...##
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Splines and wavelets on circulant graphs

2017
*
Applied and Computational Harmonic Analysis
*

Ultimately, we consider generalizations to arbitrary

doi:10.1016/j.acha.2017.10.002
fatcat:c2lxgxxz4vdhld4ryxgr62sjcu
*graphs*in the form*of**graph**approximations*, with focus on*graph**product*decompositions. ... In particular, we proceed to show how the use*of**graph**products*facilitates a multi-dimensional extension*of*the proposed constructions and*properties*. ... In particular, given an arbitrary undirected*graph*, we consider its*approximation*as the*graph**product**of*circulant*graphs*. ...##
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Learning Valued Relations from Data
[chapter]

2011
*
Advances in Intelligent and Soft Computing
*

It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types

doi:10.1007/978-3-642-24001-0_24
dblp:conf/eurofuse/WaegemanPASB11
fatcat:fid63q7ofbgytnemxwlxukfiia
*of*valued relations can be modeled, including*symmetric*... Driven by a large number*of*potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting*of*inferring relations between pairs*of*data objects ... A Kronecker*product*feature mapping was proposed for combining the features*of*pairs*of*objects that constitute a relation (edge level in a*graph*). ...##
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Subgraph densities in Markov spaces
[article]

2022
*
arXiv
*
pre-print

We generalize subgraph densities, arising in dense

arXiv:2206.04493v1
fatcat:gdartabb3zeqdcba2m7a3e46vq
*graph*limit theory, to Markov spaces (*symmetric**measures*on the square*of*a standard Borel space). ... More generally, we define an analogue*of*the set*of*homomorphisms in the form*of*a*measure*on maps*of*a finite*graph*into a Markov space. ... Since graphons can be*approximated*by finite*graphs*via sampling, and the homomorphism*measures**of*these finite*graphs**approximate*the homomorphism*measure**of*the graphon, we obtain a partial answer to ...##
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Deterministic Approximation of Random Walks in Small Space

2019
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Second, we define and analyze a generalization

doi:10.4230/lipics.approx-random.2019.42
dblp:conf/approx/MurtaghRSV19
fatcat:qbobogy745ds7b43u23fx3oj4y
*of*the derandomized square for irregular*graphs*and for sparsifying the*product**of*two distinct*graphs*. ... We give a deterministic, nearly logarithmic-space algorithm that given an undirected*graph*G, a positive integer r, and a set S*of*vertices,*approximates*the conductance*of*S in the r-step random walk ... To*measure*the*approximation*between*graphs*we use spectral*approximation*2 [23]: Definition 5. Let L, L ∈ R n×n be*symmetric*PSD matrices. ...##
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Spectral clustering with epidemic diffusion

2013
*
Physical Review E
*

We show that the replicator, an operator describing epidemic diffusion, is equivalent to the

doi:10.1103/physreve.88.042813
pmid:24229231
fatcat:bn3xge357rbshijkt277n37tte
*symmetric*normalized Laplacian*of*a reweighted*graph*with edges reweighted by the eigenvector centralities*of*... We propose a new spectral partitioning method that exploits the*properties**of*epidemic diffusion. ... This work has been funded by the Air Force Office*of*Scientific Research under contracts ...##
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Page 2095 of Mathematical Reviews Vol. , Issue 90D
[page]

1990
*
Mathematical Reviews
*

For a

*measurable*function f on [0,1] let AC(/) = {x:f is ap- proximately continuous at x}, AS(/) = {x:f is*approximately**symmetric*at x}, ASC(/) = {x: f is*approximately**symmetrically*continuous at x}, ... [Evans, Michael Jon] (1-NCS); Humke, Paul D. (1-OLAF) The*approximate**symmetric*behavior*of*real functions. Real Anal. Exchange 14 (1988/89), no. 2, 375-392. ...##
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Asymmetric Transitivity Preserving Graph Embedding

2016
*
Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '16
*

*Graph*embedding algorithms embed a

*graph*into a vector space where the structure and the inherent

*properties*

*of*the

*graph*are preserved. ... The existing

*graph*embedding methods cannot preserve the asymmetric transitivity well, which is a critical

*property*

*of*directed

*graphs*. ... Preserving the

*symmetric*transitivity in undirected

*graphs*in an embedding space is natural and straightforward, as most

*of*the distance metrics defined in the vector space possess the

*property*

*of*

*symmetric*...

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