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Minimal Representations of Order Types by Geometric Graphs [article]

Oswin Aichholzer, Martin Balko, Michael Hoffmann, Jan Kynčl, Wolfgang Mulzer, Irene Parada, Alexander Pilz, Manfred Scheucher, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl
2020 arXiv   pre-print
In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S.  ...  That is, in the geometric graph on S whose edges are the exit edges, in order to change the order type of S, at least one vertex needs to move across an exit edge.  ...  Supporting graphs in general need not be connected, and two minimal geometric graphs that are supporting for point sets with different order types can be drawings of the same abstract graph; see Fig.  ... 
arXiv:1908.05124v2 fatcat:qhifgfn2ufdq5ckfhcmx4gbeti

Drawing Algorithms for Series-Parallel Digraphs in Two and Three Dimensions [chapter]

Seok-Hee Hong, Peter Eades, Aaron Quigley, Sang-Ho Lee
1998 Lecture Notes in Computer Science  
Geometric Automorphisms of Graphs and Symmetries of Graph Drawings We need some of the terminology of permutation groups; for more details see [15] . We denote the identity permutation by I.  ...  Introduction Series parallel digraphs are one of the most common types of graphs: they appear in flow diagrams, dependency charts, and in PERT networks.  ... 
doi:10.1007/3-540-37623-2_15 fatcat:5ostqgvxlrchxf7sh5zfjik2wm

Corner-Sharing Tetrahedra for Modeling Micro-Structure [article]

Meera Sitharam, Jeremy Youngquist, Maxwell Nolan, Jörg Peters
2018 arXiv   pre-print
The paper develops a palette of simple geometry processing operations on CoSTs including graph manipulation, hierarchical refinement, randomization, and generating associated continuous representations  ...  State-of-the-art representations of volumetric multi-scale shape and structure can be classified into three broad categories: continuous, continuous-from-discrete, and discrete representations.  ...  These representations associated with the CoST graph then admit higher-order iso-parametric or iso-geometric analysis.  ... 
arXiv:1806.05528v1 fatcat:a5arrposebdilpoubdul3ju3te

Exploiting Relational Information in Social Networks using Geometric Deep Learning on Hypergraphs

Devanshu Arya, Marcel Worring
2018 Proceedings of the 2018 ACM on International Conference on Multimedia Retrieval - ICMR '18  
In these communities, some relations are much more complicated than pairwise relations, thus cannot be simply modeled by a graph; (b) there are different types of entities and relations in a social network  ...  We need a model that transfers information from a given type of relations between entities to predict other types of relations, irrespective of the type of entity.  ...  [8] relaxed eq.1 by nuclear norm minimization given by eq.2.  ... 
doi:10.1145/3206025.3206062 dblp:conf/mir/AryaW18 fatcat:efr5s4otpvc3hdcdgmxv6gu7my

A bridge-based algorithm for simultaneous primal and dual defects compression on topologically quantum-error-corrected circuits

Wei-Hsiang Tseng, Yao-Wen Chang
2022 Proceedings of the 59th ACM/IEEE Design Automation Conference  
The required resource of a TQEC circuit can be modeled as a space-time volume of a three-dimensional diagram by describing the defect movement along the time axis.  ...  Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 47%.  ...  On the same qubit in the ICM representation, the second-order measurements of distinct T gates operation should obey a time ordering [17] , the inter-T gate constraint.  ... 
doi:10.1145/3489517.3530483 fatcat:7uzr3yrjjrejrj7wjpkrzyvypy

Rigid body pose and twist scene graph founded on geometric relations semantics for robotic applications

Tinne De Laet, Herman Bruyninckx, Joris De Schutter
2013 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems  
This paper presents a scene graph for geometric relations between rigid bodies that keeps track of poses and twists of rigid bodies in the scene.  ...  The presented scene graph takes into account constraints imposed by particular coordinate representations, allows for constant poses, answers semantic pose and twist queries, and provides built-in semantic  ...  representations in wrong order, . . . ) [1] .  ... 
doi:10.1109/iros.2013.6696693 dblp:conf/iros/LaetBS13 fatcat:j2dirgv7nra6tgitct3422qp4m

Exploiting local and global geometric data relationships in Support Vector Data Description

Vasileios Mygdalis, Anastasios Tefas, Ioannis Pitas
2016 2016 23rd International Conference on Pattern Recognition (ICPR)  
Moreover, the proposed method could exploit multiple graph types, thus evolving methods to automatically determine the appropriate combination of multiple graph types could be developed. , values of ρ  ...  This can be explained by the fact that kNN graphs provide local geometric information, and fully connected graphs provide global geometric information about the training class.  ... 
doi:10.1109/icpr.2016.7899685 dblp:conf/icpr/MygdalisTP16 fatcat:h7iwl657vnf75gey3e7sj53zpu

A Graph-Theoretic Technique for Classification of Normal and Tumor Tissues Using Gene Expression Microarray Data

Saejoon Kim
2007 IEEE Engineering in Medicine and Biology Society. Conference Proceedings  
In this paper, we propose a graph-theoretic approach to the classification of normal and tumor tissues through the use of geometric representation of the graph derived from the microarray data.  ...  The accuracy of our geometric representationbased classification algorithm is shown to be comparable to that of currently known best classification algorithms for the microarray data, and in particular  ...  Geometric Representation This subsection describes how a geometric representation or a linear ordering of the similarity graph of sample vectors is computed.  ... 
doi:10.1109/iembs.2007.4353369 pmid:18003035 fatcat:x7fe6qyshjgw3bqvrvshcapgqa

Interactive graphics for the computer-aided design of dynamic systems

H. Barker, Min Chen, C. Jobling, P. Townsend
1987 Control Systems Magazine  
This paper addresses the general approach to the problem of designing an interactive environment through which graphical descriptions of dynamic systems, such as block diagrams and signal flow graphs,  ...  The use of symbolic computation for the efficient preprocessing of algebraic data for numerical design packages is also discussed.  ...  connections. minimization of the global number of bends in connections. minimization of the global length of connections. prevention of blocks being crossed by connections.  ... 
doi:10.1109/mcs.1987.1105300 fatcat:jjyzz5tetrbc7p26hxtohim4ia

Geometry Contrastive Learning on Heterogeneous Graphs [article]

Shichao Zhu, Chuan Zhou, Anfeng Cheng, Shirui Pan, Shuaiqiang Wang, Dawei Yin, Bin Wang
2022 arXiv   pre-print
GCL maximizes the mutual information between two geometric views by contrasting representations at both local-local and local-global semantic levels.  ...  Meanwhile, most existing representation learning methods embed the heterogeneous graphs into a single geometric space, either Euclidean or hyperbolic.  ...  In order to obtain a more expressive representation of heterogeneous graph, two geometric graph encoders are developed to learn representations from Euclidean and hyperbolic spaces, respectively.  ... 
arXiv:2206.12547v1 fatcat:dfjnsdw7rfcnrn3mzmvtquof3q

Selected Open Problems in Graph Drawing [chapter]

Franz Brandenburg, David Eppstein, Michael T. Goodrich, Stephen Kobourov, Giuseppe Liotta, Petra Mutzel
2004 Lecture Notes in Computer Science  
graph G so as to minimize the area of a numberingupward planar drawing of G (taken over all possible numberings of G)?  ...  Proximity Drawability Problems Recently, much attention has been devoted to the study of the combinatorial properties of different types of proximity graphs.  ...  Acknowledgements We wish to thank Emilio Di Giacomo for useful discussions and comments while preparing this collection of open problems.  ... 
doi:10.1007/978-3-540-24595-7_55 fatcat:4xhjrvq2cffufbfswpjjjtiy3a

MOLUCINATE: A Generative Model for Molecules in 3D Space [article]

Michael Arcidiacono, David Ryan Koes
2021 arXiv   pre-print
We demonstrate the utility of this method by using it to optimize molecules for desired radius of gyration.  ...  Previous generative models have focused on producing SMILES strings or 2D molecular graphs, while attempts at producing molecules in 3D have focused on reinforcement learning (RL), distance matrices, and  ...  Additionally, this work is supported by R01GM108340 from the National Institute of General Medical Sciences.  ... 
arXiv:2109.15308v2 fatcat:7zz2tag6yrhl5bc5gvebgwnupi

Sublinear Models for Graphs [article]

Brijnesh J. Jain
2014 arXiv   pre-print
The results are (i) a geometric interpretation of sublinear classifiers, (ii) a generic learning rule based on the principle of empirical risk minimization, (iii) a convergence theorem for the margin perceptron  ...  Empirical results on graph data show that sublinear models on graphs have similar properties as linear models for feature vectors.  ...  To this end, we replaced the inner product of vectors by the sublinear dot product of graphs and lifted the learning problem to the ambient Euclidean space.  ... 
arXiv:1403.2295v1 fatcat:j47l2qnm2bhdbcov3ihag3hi2a

Geometric Laplacian Eigenmap Embedding [article]

Leo Torres, Kevin S Chan, Tina Eliassi-Rad
2019 arXiv   pre-print
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks.  ...  Instead, we use the Laplacian matrix to find an embedding with geometric properties instead of spectral ones, by leveraging the so-called simplex geometry of G.  ...  For this purpose, the task of graph representation learning, or graph embedding, seeks to build a vector representation of a graph by assigning to each node a feature vector that can then be fed into any  ... 
arXiv:1905.09763v1 fatcat:rgjy5vehx5hjpgbrhqfexw3tma

One-Class Classification Based on Extreme Learning and Geometric Class Information

Alexandros Iosifidis, Vasileios Mygdalis, Anastasios Tefas, Ioannis Pitas
2016 Neural Processing Letters  
We formulate the proposed method to exploit data representations in the feature space determined by the network hidden layer outputs, as well as in ELM spaces of arbitrary dimensions.  ...  We show that the exploitation of geometric class information enhances performance.  ...  Since several types of graphs describing different types of class data relationships can be defined, we report the performance of the proposed GOC-ELM classifier for several types of graphs.  ... 
doi:10.1007/s11063-016-9541-y fatcat:xvbnyhgt5vckzkxifm6zissxpq
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