Equivalence of deterministic walks on regular lattices on the plane

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

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Groundstate threshold pc in Ising frustration systems on 2D regular lattices

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(94)90166-x ◽

1994 ◽

Vol 202 (1-2) ◽

pp. 48-67 ◽

Cited By ~ 14

Author(s):

J. Bendisch

Keyword(s):

Regular Lattices

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Mechanical Properties of Semi-Regular Lattices

Materials & Design ◽

10.1016/j.matdes.2021.110324 ◽

2021 ◽

pp. 110324

Author(s):

Milad Omidi ◽

Luc St-Pierre

Keyword(s):

Mechanical Properties ◽

Regular Lattices

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Self-similar Hierarchical Regular Lattices

Computational Science and Its Applications – ICCSA 2010 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-12165-4_19 ◽

2010 ◽

pp. 225-240

Author(s):

Carlo Cattani ◽

Ettore Laserra

Keyword(s):

Regular Lattices ◽

Self Similar

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Graph representation learning: a survey

APSIPA Transactions on Signal and Information Processing ◽

10.1017/atsip.2020.13 ◽

2020 ◽

Vol 9 ◽

Author(s):

Fenxiao Chen ◽

Yun-Cheng Wang ◽

Bin Wang ◽

C.-C. Jay Kuo

Keyword(s):

Graph Embedding ◽

Large Data ◽

Representation Learning ◽

Graph Representation ◽

Data Sets ◽

Graph Data ◽

Graph Properties ◽

Wide Range ◽

Regular Lattices ◽

Low Dimensional

Abstract Research on graph representation learning has received great attention in recent years since most data in real-world applications come in the form of graphs. High-dimensional graph data are often in irregular forms. They are more difficult to analyze than image/video/audio data defined on regular lattices. Various graph embedding techniques have been developed to convert the raw graph data into a low-dimensional vector representation while preserving the intrinsic graph properties. In this review, we first explain the graph embedding task and its challenges. Next, we review a wide range of graph embedding techniques with insights. Then, we evaluate several stat-of-the-art methods against small and large data sets and compare their performance. Finally, potential applications and future directions are presented.

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