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Representing abstract groups by powers of a graph

Walter Vogler
1986 Journal of combinatorial theory. Series B (Print)  
We deal with the problem of representing several abstract groups simultaneously by one graph as automorphism groups of its powers.  ...  ., r" of a finite group r representable iff there is a graph G and an injective mapping 4 from U:= 1 r, into the symmetric group on V(G) such that for i= l,..., n C$ I,-, is a monomorphism onto Aut G'.  ...  INTRODUCTION By a result of Frucht [ 1 ] we can represent any finite group by a graph as its automorphism group, i.e., for each finite (abstract) group r there is a graph G with Aut G N J'.  ... 
doi:10.1016/0095-8956(86)90066-3 fatcat:xzinu3doxbfzlcaksyjb7lojmm

Isotopy classification of three-dimensional embedded nets

Egon Schulte
2020 Acta Crystallographica Section A: Foundations and Advances  
This translation group T provides a geometric representation of the abstract periodicity structure on the underlying structure graph.  ...  The underlying topological structure of a net is provided by an abstract graph G, with finite or (usually) countably infinite vertex set and edge set, and in the infinite case equipped with an abstract  ...  A linear graph knot is a geometric realization in the flat torus of the labeled quotient graph of a linear periodic embedded net in Euclidean space. Image kindly provided by Davide Proserpio.  ... 
doi:10.1107/s2053273320005616 pmid:32356779 pmcid:PMC7233018 fatcat:izejjcna2jbk5lrf6n7kbbblla

Graph-Theoretical Approach for Quantifying the Large-Scale Structure of the Universe

Haruhiko Ueda, Makoto Itoh
1997 Nippon Tenmon Gakkai obun kenkyu hokoku  
For supplementary purposes we also construct a separated minimal spanning tree and a group graph, and examine the usefulness of the graph-theoretical approach.  ...  In order to examine the validity of this approach, we construct graphs based on our cosmological JV-body simulations with scale-free power-law spectra, and apply graph theory to them.  ...  Analysis of the Complexity, Order, and Degree of a Group Graph Because a group graph is not a tree graph, we can define the complexity K(G) of a group graph.  ... 
doi:10.1093/pasj/49.2.131 fatcat:yt2nagsw2nf3rce7vsc6mvovai

The Typed Graph Model [article]

Fritz Laux
2021 arXiv   pre-print
The power of this model is provided by using hyper-nodes and hyper-edges, which allows to present a data structure on different abstraction levels.  ...  We demonstrate by example the superiority of this model over the property graph data model of Hidders and other prevalent data models, namely the relational, object-oriented, and XML model.  ...  This model seems to be equivalent to (complex) nodes with properties governed by a schema. A mechanism to abstract and group sub-graphs would help to make the model easier to communicate.  ... 
arXiv:2110.00991v1 fatcat:py7dwn56sbdvnk62lskrbjnyde

The Role of Mid-Level Shape Priors in Perceptual Grouping and Image Abstraction [chapter]

Sven J. Dickinson, Alex Levinshtein, Pablo Sala, Cristian Sminchisescu
2013 Shape Perception in Human and Computer Vision  
In the third, we use a vocabulary of simple parts to both group superpixels into parts and recover the abstract shapes of the parts.  ...  The reason for this is clear: the object-independent, mid-level shape priors that form the basis of perceptual grouping are subsumed by the object-dependent, high-level shape priors defined by a target  ...  Acknowledgements The authors gratefully acknowledge the support of NSERC, Mitacs, and DARPA. Sven Dickinson would like to thank Keith Price for providing the data in Figure 1.1(b) .  ... 
doi:10.1007/978-1-4471-5195-1_1 fatcat:7nlmm7rhv5bhhmkcybmdgwv2sy

Graph Abstraction Based on Node Betweenness Centrality

Arwa M. Aldabobi, Department of Computer Science, University of Jordan, Jordan, Riad S. Jabri
2019 International Journal of Image Graphics and Signal Processing  
Graph abstraction is done by removing the nodes with their attached edges such that they have betweenness centrality lower than a certain examined threshold.  ...  There are many graph abstraction methods that are existed as solutions for problems of graphs visualization.  ...  Community structure is a well-known property in systems such that community is a group of elements that has intensive relations compared to relations with another groups of elements [3] .  ... 
doi:10.5815/ijigsp.2019.11.02 fatcat:barz7if4i5bbhgxk3nrwvb4upm

Declarative and distributed graph analytics with GRADOOP

Martin Junghanns, Max Kießling, Niklas Teichmann, Kevin Gómez, André Petermann, Erhard Rahm
2018 Proceedings of the VLDB Endowment  
Using a rich graph data model and powerful graph operators, users can declaratively express graph analytical programs for distributed execution without needing advanced programming experience or a deeper  ...  Visitors of the demo can declare graph analytical programs using the Gradoop operators and also visually experience two of our advanced operators: graph pattern matching and graph grouping.  ...  Here, we group vertices and edges by their label to find out what is connected and how. Each vertex and edge in the summary graph represents a group of vertices and edges of the input graph.  ... 
doi:10.14778/3229863.3236246 fatcat:sl5qvof6wremrjalgt44tphh44

PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells

F. Alexander Wolf, Fiona K. Hamey, Mireya Plass, Jordi Solana, Joakim S. Dahlin, Berthold Göttgens, Nikolaus Rajewsky, Lukas Simon, Fabian J. Theis
2019 Genome Biology  
Partition-based graph abstraction (PAGA) provides an interpretable graph-like map of the arising data manifold, based on estimating connectivity of manifold partitions ( https://github.com/theislab/paga  ...  We demonstrate the method by inferring structure-rich cell maps with consistent topology across four hematopoietic datasets, adult planaria and the zebrafish embryo and benchmark computational performance  ...  The kNN graph is partitioned at a desired resolution where partitions represent groups of connected cells.  ... 
doi:10.1186/s13059-019-1663-x pmid:30890159 pmcid:PMC6425583 fatcat:vn5exscyl5bhxevezn2kvsymiu

Fault Diagnosis Based on Graph Theory and Linear Discriminant Principle in Electric Power Network

Yagang ZHANG, Qian MA, Jinfang ZHANG, Jing MA, Zengping WANG
2010 Wireless Sensor Network  
In the study of fault diagnosis in electric power network, graph theory algorithms and linear discriminant technology must also have a good prospect of application.  ...  And the linear discriminant is a procedure used to classify an object into one of several a priori groupings dependent on the individual characteristics of the object.  ...  Acknowledgments This research was supported partly by Key Program of National Natural Science Foundation of China (5083 7002) and the Science Foundation for the Doctors of NCEPU.  ... 
doi:10.4236/wsn.2010.21009 fatcat:zxldxirtjbdntcxubdwxkxqmda

Diffusion wavelet embedding: A multi-resolution approach for graph embedding in vector space

Hoda Bahonar, Abdolreza Mirzaei, Richard C. Wilson
2018 Pattern Recognition  
Representative features are then extracted at each scale to provide a scale-space description of the graph.  ...  At each scale, we extract a detail subspace and a corresponding lower-scale approximation subspace to represent the graph.  ...  represented by graphs.  ... 
doi:10.1016/j.patcog.2017.09.030 fatcat:m3smz5tv6vgahc5zrjndbfnbsy

Object Categorization and the Need for Many-to-Many Matching [chapter]

Sven Dickinson, Ali Shokoufandeh, Yakov Keselman, Fatih Demirci, Diego Macrini
2005 Lecture Notes in Computer Science  
These early systems, however, were limited by their inability to bridge the representational gap between low-level image features and high-level object models, hindered by the assumption of one-to-one  ...  Object recognition systems have their roots in the AI community, and originally addressed the problem of object categorization.  ...  If we consider the space of all possible graphs formed by merging two adjacent regions, then each input exemplar gives rise to a lattice of region adjacency graphs, representing all possible region groupings  ... 
doi:10.1007/11550518_62 fatcat:b3ybc4jqdjbjnnocdmzn6f6erm

Page 2876 of Mathematical Reviews Vol. , Issue 87f [page]

1987 Mathematical Reviews  
Vogler, Walter (D-HAMB) 87f:05084 Representing abstract groups by powers of a graph. J. Combin. Theory Ser. B 40 (1986), no. 1, 81-93.  ...  The author investigates the related problem of representing simultaneously several subgroups X,,°::,X,, of a finite group X as automorphism groups of a graph G and its powers: the preblem is, given subgroups  ... 

Unraveling Protein Networks with Power Graph Analysis

Loïc Royer, Matthias Reimann, Bill Andreopoulos, Michael Schroeder, Johannes Berg
2008 PLoS Computational Biology  
Power Graphs are a novel representation of networks, which reduces network complexity by explicitly representing re-occurring network motifs.  ...  Additionally, we demonstrate the generality of Power Graph Analysis by applying it to two other types of networks.  ...  Acknowledgments Thanks to Christof Winter for detailed feedback and discussions on the biological relevance of power graphs and to Andreas Henschel, Frank Dressel and Annalisa Marsico for critique and  ... 
doi:10.1371/journal.pcbi.1000108 pmid:18617988 pmcid:PMC2424176 fatcat:eaes73hv2vbnnejquzy5pvtoxa

Selective abstraction and stochastic methods for scalable power modelling of heterogeneous systems

A. Rafiev, F. Xia, A. Iliasov, R. Gensh, A. Aalsaud, A. Romanovsky, A. Yakovlev
2016 2016 Forum on Specification and Design Languages (FDL)  
Selective abstraction and stochastic methods for scalable power modelling of heterogeneous systems.  ...  Abstract-With the increase of system complexity in both platforms and applications, power modelling of heterogeneous systems is facing grand challenges from the model scalability issue.  ...  This work is supported by EPSRC as a part of PRiME project EP/K034448/1. A. Aalsaud is supported by a postgraduate studentship from the Education Ministry of Iraq  ... 
doi:10.1109/fdl.2016.7880376 dblp:conf/fdl/RafievXIGARY16 fatcat:gauev4q2oveypdzn3me2oo4dei

Improving Efficiency in Mobile Robot Task Planning Through World Abstraction

C. Galindo, J.-A. Fernandez-Madrigal, J. Gonzalez
2004 IEEE Transactions on Robotics  
Broadly speaking, our approach works by firstly solving the task planning problem in a highly abstracted model of the environment of the robot, and then refines the solution under more detailed models  ...  This paper proposes a new approach to task planning called Hierarchical Task Planning through World Abstraction (HPWA) that, by arranging hierarchically the world representation, becomes a good complement  ...  Also, we are working on obtaining predicates not only from nodes and arcs, but also from non-structural information held by the AH-graph.  ... 
doi:10.1109/tro.2004.829480 dblp:journals/trob/GalindoFG04 fatcat:x2y6jhnd35bnnmkvapegfim6mq
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