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Probably Optimal Graph Motifs

Andreas Björklund, Petteri Kaski, Lukasz Kowalik, Marc Herbstritt
2013 Symposium on Theoretical Aspects of Computer Science  
Björklund, Kaski, Kowalik () Probably Optimal Graph Motifs STACS, Kiel, 28.02.2013 15 / 24 back.  ...  Björklund, Kaski, Kowalik () Probably Optimal Graph Motifs STACS, Kiel, 28.02.2013 3 / 24 What if there is no motif in the graph? Is there something close to the motif?  ... 
doi:10.4230/lipics.stacs.2013.20 dblp:conf/stacs/BjorklundKK13 fatcat:ylck4vhkzrhnvjjzwqlommvqty

Probably Optimal Graph Motifs *

Andreas Björklund, Petteri Kaski, Łukasz Kowalik
unpublished
The Closest Graph Motif problem encompasses several previously studied optimization variants, like Maximum Graph Motif, Min-Substitute, and Min-Add.  ...  We also introduce a new optimization variant of the problem, called Closest Graph Motif and solve it within the same time bound.  ...  Probably Optimal Graph Motifs Let W = (T, h) be a branching walk in G, let s : V (T ) → D be a consistent shading of W , and let : V (T ) → {1, 2, . . . , k} be a labelling of W .  ... 
fatcat:iuokhmexobamxfdkxb3wn6kxyq

Motif-Driven Contrastive Learning of Graph Representations [article]

Shichang Zhang, Ziniu Hu, Arjun Subramonian, Yizhou Sun
2021 arXiv   pre-print
Our framework MotIf-driven Contrastive leaRning Of Graph representations (MICRO-Graph) can: 1) use GNNs to extract motifs from large graph datasets; 2) leverage learned motifs to sample informative subgraphs  ...  To solve it, we propose to learn graph motifs, which are frequently-occurring subgraph patterns (e.g. functional groups of molecules), for better subgraph sampling.  ...  In the E-step we calculate the posterior probability , = ( = | ). In the M-step, we optimize the objective to find the optimal partition and parameter .  ... 
arXiv:2012.12533v3 fatcat:kknuji2x7zek7bsy7ziuiv5byu

A combinatorial optimization approach for diverse motif finding applications

Elena Zaslavsky, Mona Singh
2006 Algorithms for Molecular Biology  
Results: We introduce a versatile combinatorial optimization framework for motif finding that couples graph pruning techniques with a novel integer linear programming formulation.  ...  Moreover, in most cases, our approach finds provably optimal solutions to the underlying optimization problem.  ...  Acknowledgements The authors thank Stephen Altschul for help in assessing the statistical significance of discovered motifs, and the anonymous referees for their helpful suggestions.  ... 
doi:10.1186/1748-7188-1-13 pmid:16916460 pmcid:PMC1570465 fatcat:yfk3tic2y5a2rcwrxs35a6qycy

GNNInterpreter: A Probabilistic Generative Model-Level Explanation for Graph Neural Networks [article]

Xiaoqi Wang, Han-Wei Shen
2022 arXiv   pre-print
Recently, Graph Neural Networks (GNNs) have significantly advanced the performance of machine learning tasks on graphs.  ...  More specifically, with continuous relaxation of graphs and the reparameterization trick, GNNInterpreter learns a probabilistic generative graph distribution which produces the most representative graph  ...  Table 9 : 9 For each motif set, the average predicted class probability of each class is computed by averaging over 5000 graphs containing the corresponding motif.  ... 
arXiv:2209.07924v1 fatcat:fpidyeugb5aqpnnmwgka75y6xa

Topological motifs populate complex networks through grouped attachment

Jaejoon Choi, Doheon Lee
2018 Scientific Reports  
: the Erdös-Rényi, small-world, scale-free, popularity-similarity-optimization, and nonuniform popularity-similarity-optimization models.  ...  Recently, two hyperbolic geometrical models have been developed: popularity-similarity-optimization (PSO) 7 , and nonuniform popularity-similarity-optimization (nPSO) 8,9 models.  ...  Among the nodes in the graph G, we select nodes with a probability p/q to be connected, and for every selected nodes, we connect to the nodes in the graph F with a probability q (p < q < 1).  ... 
doi:10.1038/s41598-018-30845-4 pmid:30140017 pmcid:PMC6107624 fatcat:id6xekreezheloarahz44e5t4e

MotifCut: regulatory motifs finding with maximum density subgraphs

E. Fratkin, B. T. Naughton, D. L. Brutlag, S. Batzoglou
2006 Bioinformatics  
Results: We present MotifCut, a graph-theoretic approach to motif finding leading to a convex optimization problem with a polynomial time solution.  ...  Most existing methods formulate motif finding as an intractable optimization problem and rely either on expectation maximization (EM) or on local heuristic searches.  ...  The probability of a k-mer belonging to a motif given its mutation distance to a motif k-mer.  ... 
doi:10.1093/bioinformatics/btl243 pmid:16873465 fatcat:wwfrirzimfal3lpqefhdz4qtli

M-Evolve: Structural-Mapping-Based Data Augmentation for Graph Classification [article]

Jiajun Zhou, Jie Shen, Shanqing Yu, Guanrong Chen, Qi Xuan
2020 arXiv   pre-print
To improve this, we introduce data augmentation on graphs (i.e. graph augmentation) and present four methods:random mapping, vertex-similarity mapping, motif-random mapping and motif-similarity mapping  ...  Furthermore, we propose a generic model evolution framework, named M-Evolve, which combines graph augmentation, data filtration and model retraining to optimize pre-trained graph classifiers.  ...  Motif-Random Mapping Graph motifs are sub-graphs that repeat themselves in a specific graph or even among various graphs.  ... 
arXiv:2007.05700v2 fatcat:m3marhsgljemxflwydlqjwyk3i

Predicting sequence and structural specificities of RNA binding regions recognized by splicing factor SRSF1

Xin Wang, Liran Juan, Junjie Lv, Kejun Wang, Jeremy R Sanford, Yunlong Liu
2011 BMC Genomics  
The unpaired probabilities, the probabilities of not forming pairs, are significantly higher than negative controls and the flanking sequence surrounding the binding site, indicating that SRSF1 proteins  ...  Conclusion: In this study, we presented a computational model to predict the sequence consensus and optimal RNA secondary structure for protein-RNA binding regions.  ...  base pairing probability of k bases in the motif θ = (θ i ); and 4) the penalty for the deviation from the optimal base pairing probability a.  ... 
doi:10.1186/1471-2164-12-s5-s8 pmid:22369183 pmcid:PMC3287504 fatcat:vtljbdv2xvdrvc26jyaqnawgra

MOTIF-Driven Contrastive Learning of Graph Representations

Arjun Subramonian
2021 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We propose a MOTIF-driven contrastive framework to pretrain a graph neural network in a self-supervised manner so that it can automatically mine motifs from large graph datasets.  ...  Our framework achieves state-of-the-art results on various graph-level downstream tasks with few labels, like molecular property prediction.  ...  We predict the probabilities of each subgraph belonging to the optimal clusters via representation-center similarity and learn subgraph representations to be more similar or dissimilar to the appropriate  ... 
doi:10.1609/aaai.v35i18.17986 fatcat:67kxuaqvvvenvepjow4jbdsd3m

Inherent limits on optimization and discovery in physical systems

Vladan Mlinar
2014 Annals of Physics  
We find inherent limits to the potential for optimization of a given system and its approximate representations by motifs, and the ability to reconstruct the full system given approximate representations  ...  Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed.  ...  as: 3, 5, 17 I ve (G) = − Nm i Nm j p ij log 2 (p ij ), by assigning probabilities to each motif, where p ij is a discrete joint probability distribution that depends on vertices and edges within the  ... 
doi:10.1016/j.aop.2014.10.008 fatcat:j57pjeezxjan5kwvnhri2mzsvi

Towards a Decomposition-Optimal Algorithm for Counting and Sampling Arbitrary Motifs in Sublinear Time [article]

Amartya Shankha Biswas, Talya Eden, Ronitt Rubinfeld
2021 arXiv   pre-print
We consider the problem of sampling and approximately counting an arbitrary given motif H in a graph G, where access to G is given via queries: degree, neighbor, and pair, as well as uniform edge sample  ...  We present a new algorithm for sampling and approximately counting arbitrary motifs which, up to poly(log n) factors, is always at least as good as previous results, and for most graphs G is strictly better  ...  There exists a motif H D , with an optimal decomposition D, and a family of graphs G over n vertices and m edges, as follows.  ... 
arXiv:2107.06582v2 fatcat:4u2fpjlqqbgibgh2ze3f4cxr7e

Cyclic transitions between higher order motifs underlie sustained activity in asynchronous sparse recurrent networks [article]

Kyle Bojanek, Yuqing Zhu, Jason MacLean
2019 bioRxiv   pre-print
If the network fails to engage the dynamical regime characterized by a recurring stable pattern of motif dominance, spiking activity ceased.  ...  We find that stereotyped low variance cyclic transitions between three isomorphic triangle motifs, quantified as a Markov process, are required for sustained activity.  ...  We searched for 467 the optimal probability of connection from excitatory to inhibitory units, p e→i , and the 468 optimal probability of connection from inhibitory to excitatory units, p i→e , such that  ... 
doi:10.1101/777219 fatcat:7w6skrk66bbjbje7cil4kqmoiu

Mixed Random Sampling of Frames method for counting number of motifs [article]

M. N. Yudina, V. N. Zadorozhnyi, E. B. Yudin
2019 arXiv   pre-print
These networks are represented in the form of directed and undirected simple graphs. Exact calculating requires huge computational resources for such large graphs.  ...  A method for calculating the frequencies of network motifs using the Monte Carlo method with control of the accuracy of calculations is proposed.  ...  Using the value  calculated by this formula in (1), we calculate the optimal estimate of the number n of motif instances in the graph.  ... 
arXiv:1904.02483v1 fatcat:c7ia3h75ffa3jgmopabfe6xqpa

Subgraph Covers: An Information-Theoretic Approach to Motif Analysis in Networks

Anatol E. Wegner
2014 Physical Review X  
Some recently introduced random graph models that can incorporate significant densities of motifs have natural formulations in terms of subgraph covers and the presented approach can be used to match networks  ...  To prove the practical value of our approach we also present a heuristic for the resulting NP-hard optimization problem and give results for several real world networks.  ...  McKay were used in gener-ating the various isomorphism classes used in our analysis and the graph-tool [20] Python package developed by Tiago de Paula Peixoto for finding subgraphs and manipulating graphs  ... 
doi:10.1103/physrevx.4.041026 fatcat:mvemsywsubcjdloy7ohgzvndsa
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