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Journal articles on the topic 'Graph dynamics'

Author: Grafiati

Published: 25 May 2024

Last updated: 25 July 2025

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1

Huang, Xueqin, Xianqiang Zhu, Xiang Xu, Qianzhen Zhang, and Ailin Liang. "Parallel Learning of Dynamics in Complex Systems." Systems 10, no. 6 (2022): 259. http://dx.doi.org/10.3390/systems10060259.

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Dynamics always exist in complex systems. Graphs (complex networks) are a mathematical form for describing a complex system abstractly. Dynamics can be learned efficiently from the structure and dynamics state of a graph. Learning the dynamics in graphs plays an important role in predicting and controlling complex systems. Most of the methods for learning dynamics in graphs run slowly in large graphs. The complexity of the large graph’s structure and its nonlinear dynamics aggravate this problem. To overcome these difficulties, we propose a general framework with two novel methods in this pape

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Li, Jintang, Zhouxin Yu, Zulun Zhu, et al. "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 7 (2023): 8588–96. http://dx.doi.org/10.1609/aaai.v37i7.26034.

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Recent years have seen a surge in research on dynamic graph representation learning, which aims to model temporal graphs that are dynamic and evolving constantly over time. However, current work typically models graph dynamics with recurrent neural networks (RNNs), making them suffer seriously from computation and memory overheads on large temporal graphs. So far, scalability of dynamic graph representation learning on large temporal graphs remains one of the major challenges. In this paper, we present a scalable framework, namely SpikeNet, to efficiently capture the temporal and structural pa

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Ahmed, Mouhamadou WADE. "Tight bounds on exploration of constantly connected cacti-paths." World Journal of Advanced Research and Reviews 12, no. 1 (2021): 355–61. https://doi.org/10.5281/zenodo.5594859.

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In this paper, we study the necessary and sufficient time to explore constantly connected dynamics graphs by a mobile entity (agent). A dynamic graph is constantly connected if for each time units, there exists a stable connected spanning tree [10]. We focus on the case where the underlying graph is a cactus-path (graph reduced to a path of  rings in which two neighbor rings have at most one vertex in common) and we assume that the agent knows the dynamics of the graph. We show that time units are necessary and sufficient to explore any constantly connected dynamic graph based on the cact

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Ahmed Mouhamadou WADE. "Tight bounds on exploration of constantly connected cacti-paths." World Journal of Advanced Research and Reviews 12, no. 1 (2021): 355–61. http://dx.doi.org/10.30574/wjarr.2021.12.1.0534.

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In this paper, we study the necessary and sufficient time to explore constantly connected dynamics graphs by a mobile entity (agent). A dynamic graph is constantly connected if for each time units, there exists a stable connected spanning tree [10]. We focus on the case where the underlying graph is a cactus-path (graph reduced to a path of k rings in which two neighbor rings have at most one vertex in common) and we assume that the agent knows the dynamics of the graph. We show that 5n - Θ(1) time units are necessary and sufficient to explore any constantly connected dynamic graph based on th

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Mouhamadou Wade, Ahmed. "EXPLORATION WITH RETURN OF HIGHLY DYNAMIC NETWORKS." International Journal of Advanced Research 9, no. 10 (2021): 315–19. http://dx.doi.org/10.21474/ijar01/13550.

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In this paper, we study the necessary and sufficient time to explore with return constantly connected dynamic networks modelled by a dynamic graphs. Exploration with return consists, for an agent operating in a dynamic graph, of visiting all the vertices of the graph and returning to the starting vertex. We show that for constantly connected dynamic graphs based on a ring of sizen,3n-4 time units are necessary and sufficient to explore it. Assuming that the agent knows the dynamics of the graph.

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Di Ianni, Miriam. "Game of Life-like Opinion Dynamics: Generalizing the Underpopulation Rule." AppliedMath 3, no. 1 (2022): 10–36. http://dx.doi.org/10.3390/appliedmath3010002.

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Graph dynamics for a node-labeled graph is a set of updating rules describing how the labels of each node in the graph change in time as a function of the global set of labels. The underpopulation rule is graph dynamics derived by simplifying the set of rules constituting the Game of Life. It is known that the number of label configurations met by a graph during the dynamic process defined by such rule is bounded by a polynomial in the size of the graph if the graph is undirected. As a consequence, predicting the labels evolution is an easy problem (i.e., a problem in P) in such a case. In thi

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Zhang, Lei, Zhiqian Chen, Chang-Tien Lu, and Liang Zhao. "From “Dynamics on Graphs” to “Dynamics of Graphs”: An Adaptive Echo-State Network Solution (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 11 (2022): 13111–12. http://dx.doi.org/10.1609/aaai.v36i11.21692.

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Many real-world networks evolve over time, which results in dynamic graphs such as human mobility networks and brain networks. Usually, the “dynamics on graphs” (e.g., node attribute values evolving) are observable, and may be related to and indicative of the underlying “dynamics of graphs” (e.g., evolving of the graph topology). Traditional RNN-based methods are not adaptive or scalable for learn- ing the unknown mappings between two types of dynamic graph data. This study presents a AD-ESN, and adaptive echo state network that can automatically learn the best neural net- work architecture fo

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Chen, Haiyan, and Fuji Zhang. "Spectral Dynamics of Graph Sequences Generated by Subdivision and Triangle Extension." Electronic Journal of Linear Algebra 32 (February 6, 2017): 454–63. http://dx.doi.org/10.13001/1081-3810.3583.

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For a graph G and a unary graph operation X, there is a graph sequence \G_k generated by G_0=G and G_{k+1}=X(G_k). Let Sp({G_k}) denote the set of normalized Laplacian eigenvalues of G_k. The set of limit points of \bigcup_{k=0}^\infty Sp(G_k)$, $\liminf_{k\rightarrow\infty}Sp(G_k) and $\limsup_{k\rightarrow \infty}Sp(G_k)$ are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained that the spectral dynamic of graph sequence generated by subdivision is determined by a quadratic function, which is closely related to the the w

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Fahrenthold, E. P., and J. D. Wargo. "Lagrangian Bond Graphs for Solid Continuum Dynamics Modeling." Journal of Dynamic Systems, Measurement, and Control 116, no. 2 (1994): 178–92. http://dx.doi.org/10.1115/1.2899209.

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The limitations of existing continuum bond graph modeling techniques have effectively precluded their use in large order problems, where nonrepetitive graph structures and causal patterns are normally present. As a result, despite extensive publication of bond graph models for continuous systems simulations, bond graph methods have not offered a viable alternative to finite element analysis for the vast majority of practical problems. However, a new modeling approach combining Lagrangian (mass fixed) bond graphs with a selected finite element discretization scheme allows for direct simulation

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Chen, Lanlan, Kai Wu, Jian Lou, and Jing Liu. "Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-Time Dynamics." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (2024): 8292–301. http://dx.doi.org/10.1609/aaai.v38i8.28670.

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Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating graph neural networks with ordinary differential equations has demonstrated promising performance. However, they disregard the crucial signed information potential on graphs, impeding their capacity to accurately capture real-world phenomena and leading to subpar outcomes. In response, we introduce a novel approach: a signed graph neural ordinary differentia

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Chen, Libin, Luyao Wang, Chengyi Zeng, Hongfu Liu, and Jing Chen. "DHGEEP: A Dynamic Heterogeneous Graph-Embedding Method for Evolutionary Prediction." Mathematics 10, no. 22 (2022): 4193. http://dx.doi.org/10.3390/math10224193.

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Current graph-embedding methods mainly focus on static homogeneous graphs, where the entity type is the same and the topology is fixed. However, in real networks, such as academic networks and shopping networks, there are typically various types of nodes and temporal interactions. The dynamical and heterogeneous components of graphs in general contain abundant information. Currently, most studies on dynamic graphs do not sufficiently consider the heterogeneity of the network in question, and hence the semantic information of the interactions between heterogeneous nodes is missing in the graph

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SAXENA, NITIN, SIMONE SEVERINI, and IGOR E. SHPARLINSKI. "PARAMETERS OF INTEGRAL CIRCULANT GRAPHS AND PERIODIC QUANTUM DYNAMICS." International Journal of Quantum Information 05, no. 03 (2007): 417–30. http://dx.doi.org/10.1142/s0219749907002918.

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The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system whose hamiltonian is identical to the adjacency matrix of a circulant graph is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds

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Arrighi, Pablo, and Gilles Dowek. "Causal graph dynamics." Information and Computation 223 (February 2013): 78–93. http://dx.doi.org/10.1016/j.ic.2012.10.019.

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Mai, Weimin, Junxin Chen, and Xiang Chen. "Time-Evolving Graph Convolutional Recurrent Network for Traffic Prediction." Applied Sciences 12, no. 6 (2022): 2842. http://dx.doi.org/10.3390/app12062842.

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Accurate traffic prediction is crucial to the construction of intelligent transportation systems. This task remains challenging because of the complicated and dynamic spatiotemporal dependency in traffic networks. While various graph-based spatiotemporal networks have been proposed for traffic prediction, most of them rely on predefined graphs from different views or static adaptive matrices. Some implicit dynamics of inter-node dependency may be neglected, which limits the performance of prediction. To address this problem and make more accurate predictions, we propose a traffic prediction mo

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15

Yang, Yu, An Wang, Hua Wang, Wei-Ting Zhao, and Dao-Qiang Sun. "On Subtrees of Fan Graphs, Wheel Graphs, and “Partitions” of Wheel Graphs under Dynamic Evolution." Mathematics 7, no. 5 (2019): 472. http://dx.doi.org/10.3390/math7050472.

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The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries on evolutionary dynamics, we consider the subtree problems of fan graphs, wheel graphs, and the class of graphs obtained from “partitioning” wheel graphs under dynamic evolution. The enumeration of these subtree numbers is done through the so-called subtree generation functions of graphs. With the enumerative result, we briefly explore the extremal

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Sun, Li, Zhongbao Zhang, Jiawei Zhang, et al. "Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (2021): 4375–83. http://dx.doi.org/10.1609/aaai.v35i5.16563.

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Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling uncertainty. To bridge this gap, we propose to learn dynamic graph representations in hyperbolic space, for the first time, which aims to infer stochastic node representations. Working with hyperbolic space, we present a novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TG

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Pan, Liming, Cheng Shi, and Ivan Dokmanic. "A Graph Dynamics Prior for Relational Inference." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 13 (2024): 14508–16. http://dx.doi.org/10.1609/aaai.v38i13.29366.

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Relational inference aims to identify interactions between parts of a dynamical system from the observed dynamics. Current state-of-the-art methods fit the dynamics with a graph neural network (GNN) on a learnable graph. They use one-step message-passing GNNs---intuitively the right choice since non-locality of multi-step or spectral GNNs may confuse direct and indirect interactions. But the effective interaction graph depends on the sampling rate and it is rarely localized to direct neighbors, leading to poor local optima for the one-step model. In this work, we propose a graph dynamics prior

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Zhu, Jiawei, Bo Li, Zhenshi Zhang, Ling Zhao, and Haifeng Li. "High-Order Topology-Enhanced Graph Convolutional Networks for Dynamic Graphs." Symmetry 14, no. 10 (2022): 2218. http://dx.doi.org/10.3390/sym14102218.

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Understanding the evolutionary mechanisms of dynamic graphs is crucial since dynamic is a basic characteristic of real-world networks. The challenges of modeling dynamic graphs are as follows: (1) Real-world dynamics are frequently characterized by group effects, which essentially emerge from high-order interactions involving groups of entities. Therefore, the pairwise interactions revealed by the edges of graphs are insufficient to describe complex systems. (2) The graph data obtained from real systems are often noisy, and the spurious edges can interfere with the stability and efficiency of

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Nair, Aditya G., and Kunihiko Taira. "Network-theoretic approach to sparsified discrete vortex dynamics." Journal of Fluid Mechanics 768 (March 10, 2015): 549–71. http://dx.doi.org/10.1017/jfm.2015.97.

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We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters in

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20

Alrawayati, Hawa Ahmed, and Ümit Tokeşer. "Spectral Integral Variation of Graph Theory." Asian Journal of Mathematics and Computer Research 32, no. 2 (2025): 151–60. https://doi.org/10.56557/ajomcor/2025/v32i29173.

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Spectral integral variation in graph theory explores the interplay between the spectral properties of graphs and their topological and geometrical characteristics. This study focuses on the eigenvalues and eigenvectors of graph-related matrices, such as the adjacency matrix and the Laplacian matrix, and their implications for understanding graph structure, connectivity, and dynamics. By examining integral variations, we establish a framework for analyzing how spectral properties change under perturbations, such as edge weight modifications and graph transformations. This paper discusses the si

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PREVITE, JOSEPH P. "Graph substitutions." Ergodic Theory and Dynamical Systems 18, no. 3 (1998): 661–85. http://dx.doi.org/10.1017/s0143385798108234.

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In 1984, Gromov (see [4] and [6]) introduced the idea of subdividing a ‘branching’ polyhedron into smaller cells and replacing these cells by more complex objects, reminiscent of the growth of multicellular organisms in biology. The simplest situation of this kind is a graph substitution which replaces certain subgraphs in a graph $G$ by bigger finite graphs. The most basic graph substitution is a vertex replacement rule which replaces certain vertices of $G$ with finite graphs. This paper develops a framework for studying vertex replacements and discusses the asymptotic behavior of iterated v

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SARKAR, Prosanta, Sourav MONDAL, Nilanjan DE, and Anita PAL. "(a,b)- Zagreb index of some special graph." Revue Roumaine de Chimie 65, no. 11 (2021): 1045–55. http://dx.doi.org/10.33224/rrch.2020.65.11.09.

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In the past few years, graph theory has emerged as one of the most powerful mathematical tools to model many types of relations and process dynamics in computer science, biological and social systems. Generally, a graph is depicted as a set of nodes which is called vertices connected by lines are called edges. A topological index is the numerical parameter of a graph that characterizes its topology and it is usually graph invariant. In this paper, we compute some important classes vertex degree-based graph invariants using the Zagreb index of some special graphs such as the co-normal product o

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Chen, Lei, Jing Zhang, and Li-Jun Cai. "Overlapping community detection based on link graph using distance dynamics." International Journal of Modern Physics B 32, no. 03 (2018): 1850015. http://dx.doi.org/10.1142/s0217979218500157.

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The distance dynamics model was recently proposed to detect the disjoint community of a complex network. To identify the overlapping structure of a network using the distance dynamics model, an overlapping community detection algorithm, called L-Attractor, is proposed in this paper. The process of L-Attractor mainly consists of three phases. In the first phase, L-Attractor transforms the original graph to a link graph (a new edge graph) to assure that one node has multiple distances. In the second phase, using the improved distance dynamics model, a dynamic interaction process is introduced to

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Bai, Wenjun. "Smoothness Harmonic: A Graph-Based Approach to Reveal Spatiotemporal Patterns of Cortical Dynamics in fMRI Data." Applied Sciences 13, no. 12 (2023): 7130. http://dx.doi.org/10.3390/app13127130.

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Despite fMRI data being interpreted as time-varying graphs in graph analysis, there has been more emphasis on learning sophisticated node embeddings and complex graph structures rather than providing a macroscopic description of cortical dynamics. In this paper, I introduce the notion of smoothness harmonics to capture the slowly varying cortical dynamics in graph-based fMRI data in the form of spatiotemporal smoothness patterns. These smoothness harmonics are rooted in the eigendecomposition of graph Laplacians, which reveal how low-frequency-dominated fMRI signals propagate across the cortex

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Mariumuthu, G., and M. S. Saraswathy. "Dynamics of Boundary Graphs." Journal of Scientific Research 5, no. 3 (2013): 447–55. http://dx.doi.org/10.3329/jsr.v5i3.14866.

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In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. A vertex v is a boundary vertex of a vertex u if for all The boundary graph B(G) based on a connected graph G is a simple graph which has the vertex set as in G. Two vertices u and v are adjacent in B(G) if either u is a boundary of v or v is a boundary of u. If G is disconnected, then each vertex in a component is adjacent to all other vertices in the other components and is adjacent to all of its boundary vertices within the component. Given a positive integer m, the mth iterat

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Chayes, Jennifer. "Mathematics of Web science: structure, dynamics and incentives." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1987 (2013): 20120377. http://dx.doi.org/10.1098/rsta.2012.0377.

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Dr Chayes’ talk described how, to a discrete mathematician, ‘all the world’s a graph, and all the people and domains merely vertices’. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online

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XING, CHANGMING, and LIN YANG. "RANDOM WALKS IN HETEROGENEOUS WEIGHTED PSEUDO-FRACTAL WEBS WITH THE SAME WEIGHT SEQUENCE." Fractals 27, no. 06 (2019): 1950089. http://dx.doi.org/10.1142/s0218348x19500890.

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Intuitively, link weight could affect the dynamics of the network. However, the theoretical research on the effects of link weight on network dynamics is still rare. In this paper, we present two heterogeneous weighted pseudo-fractal webs controlled by two weight parameters [Formula: see text] and [Formula: see text] ([Formula: see text]). Both graph models are scale-free deterministic graphs, and they have the same weight sequence when [Formula: see text] and [Formula: see text] are fixed. Based on their self-similar graph structure, we study the effect of heterogeneous weight on the random w

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Raberto, Marco, Fabio Rapallo, and Enrico Scalas. "Semi-Markov Graph Dynamics." PLoS ONE 6, no. 8 (2011): e23370. http://dx.doi.org/10.1371/journal.pone.0023370.

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Kang, Xinning. "Dynamic Adjustment of Mobile Ocean Freight Rates Based on Big Data." International Journal of Interactive Mobile Technologies (iJIM) 19, no. 13 (2025): 96–110. https://doi.org/10.3991/ijim.v19i13.56593.

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Amidst the intensifying competition in the shipping industry and the ongoing digitalization of global trade, ocean freight rates—characterized as multivariate time series—are influenced by a complex interplay of factors including port network structures, market supply and demand dynamics, and transportation costs. Traditional static pricing strategies have proven inadequate in adapting to the rapidly evolving market conditions. Accurate freight rate forecasting has emerged as a critical prerequisite for enabling dynamic adjustment strategies. However, conventional time series models often fail

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Yuan, Haonan, Qingyun Sun, Zhaonan Wang, et al. "DG-Mamba: Robust and Efficient Dynamic Graph Structure Learning with Selective State Space Models." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 21 (2025): 22272–80. https://doi.org/10.1609/aaai.v39i21.34382.

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Dynamic graphs exhibit intertwined spatio-temporal evolutionary patterns, widely existing in the real world. Nevertheless, the structure incompleteness, noise, and redundancy result in poor robustness for Dynamic Graph Neural Networks (DGNNs). Dynamic Graph Structure Learning (DGSL) offers a promising way to optimize graph structures. However, aside from encountering unacceptable quadratic complexity, it overly relies on heuristic priors, making it hard to discover underlying predictive patterns. How to efficiently refine the dynamic structures, capture intrinsic dependencies, and learn robust

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Kaval, Burak, and Alpay Kırlangıç. "Domination Scattering Number in Graphs." Journal of New Theory, no. 49 (December 31, 2024): 53–61. https://doi.org/10.53570/jnt.1563823.

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Scattering number measures the stability of a graph by determining how well vertices are spread throughout the graph. However, it may not always be distinctive for different graphs, especially when comparing the same scattering numbers. In this study, we aim to provide a more nuanced and sensitive measure of stability for graphs by introducing domination scattering numbers, a new measure of graph stability. This parameter likely captures additional structural characteristics or dynamics within the graph that contribute to its stability or resilience. Moreover, we investigate the domination sca

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Xu, Chunyan, Rong Liu, Tong Zhang, Zhen Cui, Jian Yang, and Chunlong Hu. "Dual-Stream Structured Graph Convolution Network for Skeleton-Based Action Recognition." ACM Transactions on Multimedia Computing, Communications, and Applications 17, no. 4 (2021): 1–22. http://dx.doi.org/10.1145/3450410.

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In this work, we propose a dual-stream structured graph convolution network ( DS-SGCN ) to solve the skeleton-based action recognition problem. The spatio-temporal coordinates and appearance contexts of the skeletal joints are jointly integrated into the graph convolution learning process on both the video and skeleton modalities. To effectively represent the skeletal graph of discrete joints, we create a structured graph convolution module specifically designed to encode partitioned body parts along with their dynamic interactions in the spatio-temporal sequence. In more detail, we build a se

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Changaival, Boonyarit, Martin Rosalie, Grégoire Danoy, Kittichai Lavangnananda, and Pascal Bouvry. "Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics." International Journal of Bifurcation and Chaos 27, no. 14 (2017): 1750215. http://dx.doi.org/10.1142/s0218127417502157.

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Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs

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Genova, Daniela, Hendrik Jan Hoogeboom, and Nataša Jonoska. "Companions and an Essential Motion of a Reaction System." Fundamenta Informaticae 175, no. 1-4 (2020): 187–99. http://dx.doi.org/10.3233/fi-2020-1953.

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For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-out subgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-conte

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AN HUEF, ASTRID, MARCELO LACA, IAIN RAEBURN, and AIDAN SIMS. "KMS states on the -algebras of reducible graphs." Ergodic Theory and Dynamical Systems 35, no. 8 (2014): 2535–58. http://dx.doi.org/10.1017/etds.2014.52.

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We consider the dynamics on the $C^{\ast }$-algebras of finite graphs obtained by lifting the gauge action to an action of the real line. Enomoto, Fujii and Watatani [KMS states for gauge action on ${\mathcal{O}}_{A}$. Math. Japon.29 (1984), 607–619] proved that if the vertex matrix of the graph is irreducible, then the dynamics on the graph algebra admits a single Kubo–Martin–Schwinger (KMS) state. We have previously studied the dynamics on the Toeplitz algebra, and explicitly described a finite-dimensional simplex of KMS states for inverse temperatures above a critical value. Here we study t

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Huang, Yicong, and Zhuliang Yu. "Representation Learning for Dynamic Functional Connectivities via Variational Dynamic Graph Latent Variable Models." Entropy 24, no. 2 (2022): 152. http://dx.doi.org/10.3390/e24020152.

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Latent variable models (LVMs) for neural population spikes have revealed informative low-dimensional dynamics about the neural data and have become powerful tools for analyzing and interpreting neural activity. However, these approaches are unable to determine the neurophysiological meaning of the inferred latent dynamics. On the other hand, emerging evidence suggests that dynamic functional connectivities (DFC) may be responsible for neural activity patterns underlying cognition or behavior. We are interested in studying how DFC are associated with the low-dimensional structure of neural acti

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Faizliev, Alexey, Vladimir Balash, Vladimir Petrov, Alexey Grigoriev, Dmitriy Melnichuk, and Sergei Sidorov. "Stability Analysis of Company Co-Mention Network and Market Graph Over Time Using Graph Similarity Measures." Journal of Open Innovation: Technology, Market, and Complexity 5, no. 3 (2019): 55. http://dx.doi.org/10.3390/joitmc5030055.

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The aim of the paper is to provide an analysis of news and financial data using their network representation. The formation of network structures from data sources is carried out using two different approaches: by building the so-called market graph in which nodes represent financial assets (e.g., stocks) and the edges between nodes stand for the correlation between the corresponding assets, by constructing a company co-mention network in which any two companies are connected by an edge if a news item mentioning both companies has been published in a certain period of time. Topological changes

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Samanta, B., and A. Mukherjee. "Analysis of Acoustoelastic Systems Using Modal Bond Graphs." Journal of Dynamic Systems, Measurement, and Control 112, no. 1 (1990): 108–15. http://dx.doi.org/10.1115/1.2894126.

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A procedure is presented to study the dynamics of acoustoelastic systems within the framework of bond graph technique. The substructures, acoustic and structural, are modeled individually in form of bond graphs that are coupled through suitable elements satisfying the conditions at the interfaces. From this bond graph a second stage modal decomposition is performed to represent the overall system in yet another bond graph that can be analyzed to obtain the overall system dynamics. The scope for two-stage modal truncation makes the procedure suitable for analyzing acoustoelastic systems that ar

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Wang, Mingjie, Yifan Huo, Junhong Zheng, and Lili He. "SC-TKGR: Temporal Knowledge Graph-Based GNN for Recommendations in Supply Chains." Electronics 14, no. 2 (2025): 222. https://doi.org/10.3390/electronics14020222.

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Graph neural networks (GNNs) are widely used in recommendation systems to improve prediction performance, especially in scenarios with diverse behaviors and complex user interactions within supply chains. However, while existing models have achieved certain success in capturing the temporal and dynamic aspects of supply chain behaviors, challenges remain in effectively addressing the time-sensitive fluctuations of market demands and user preferences. Motivated by these challenges, we propose SC-TKGR, a supply chain recommendation framework based on temporal knowledge graphs. It employs enhance

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Blachowski, B., and W. Gutkowski. "Graph based discrete optimization in structural dynamics." Bulletin of the Polish Academy of Sciences: Technical Sciences 62, no. 1 (2014): 91–102. http://dx.doi.org/10.2478/bpasts-2014-0011.

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Abstract In this study, a relatively simple method of discrete structural optimization with dynamic loads is presented. It is based on a tree graph, representing discrete values of the structural weight. In practical design, the number of such values may be very large. This is because they are equal to the combination numbers, arising from numbers of structural members and prefabricated elements. The starting point of the method is the weight obtained from continuous optimization, which is assumed to be the lower bound of all possible discrete weights. Applying the graph, it is possible to fin

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Mosterman, P. J. "HYBRSIM—a modelling and simulation environment for hybrid bond graphs." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 216, no. 1 (2002): 35–46. http://dx.doi.org/10.1243/0959651021541417.

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Bond graphs are a powerful formalism to model continuous dynamics of physical systems. Hybrid bond graphs introduce an ideal switching element, the controlled junction, to approximate continuous behaviour that is too complex for numerical analysis (e.g. because of non-linearities or steep gradients). HYBRSIM is a tool for hybrid bond graph modelling and simulation implemented in Java and is documented in this paper. It performs event detection and location based on a bisectional search, handles run-time causality changes, including derivative causality, performs physically consistent (re-)init

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Amorim, Tiago de Albuquerque, and Miriam Manoel. "The realisation of admissible graphs for coupled vector fields." Nonlinearity 37, no. 1 (2023): 015004. http://dx.doi.org/10.1088/1361-6544/ad0ca4.

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Abstract In a coupled network cells can interact in several ways. There is a vast literature from the last 20 years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence relation on the set of vertices that enables a characterisation of the admissible vector fields that rules the network dynamics. The present work goes in the direction of answering an inverse problem: for n ⩾ 2 , any mapping on R n can be realised as an admissible vector field for some graph with the number of vertices depending on (but not necessarily e

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Yuan, Feng, Penglin Zhang, Qi Zhang, Yu Zhang, and Anni Wang. "Representing the Spatiotemporal State Evolution of Geographic Entities as a Multi-Level Graph." ISPRS International Journal of Geo-Information 14, no. 7 (2025): 252. https://doi.org/10.3390/ijgi14070252.

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The geographic knowledge graph offers a structured framework for mining and discovering spatiotemporal knowledge, which is of great significance for understanding geographic dynamics. However, existing geographic knowledge graphs still encounter significant challenges in comprehensive expression of spatiotemporal elements and understanding the intricate relationships and dynamic evolution among geographic entities, space, and time. Therefore, a Spatiotemporal Evolution Hierarchical Representation Graph (STEHRG) is proposed, which consists of three layers: a spatiotemporal ontology layer, a spa

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Parmelee, Caitlyn, Samantha Moore, Katherine Morrison, and Carina Curto. "Core motifs predict dynamic attractors in combinatorial threshold-linear networks." PLOS ONE 17, no. 3 (2022): e0264456. http://dx.doi.org/10.1371/journal.pone.0264456.

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Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. In prior work, we have developed a detailed mathematical theory relating stable and unstable fixed points of CTLNs to graph-theoretic properties of the underlying network. Here we find that a special type of fixed points, corresponding to core motifs, are predictive of both static and dynamic attractors. Moreover, the at

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Sun, Mengzhu, Xi Zhang, Jiaqi Zheng, and Guixiang Ma. "DDGCN: Dual Dynamic Graph Convolutional Networks for Rumor Detection on Social Media." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (2022): 4611–19. http://dx.doi.org/10.1609/aaai.v36i4.20385.

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Detecting rumors on social media has become particular important due to the rapid dissemination and adverse impacts on our lives. Though a set of rumor detection models have exploited the message propagation structural or temporal information, they seldom model them altogether to enjoy the best of both worlds. Moreover, the dynamics of knowledge information associated with the comments are not involved, either. To this end, we propose a novel Dual-Dynamic Graph Convolutional Networks, termed as DDGCN, which can model the dynamics of messages in propagation as well as the dynamics of the backgr

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Pan, Zhiqiang, Wanyu Chen, and Honghui Chen. "Dynamic Graph Learning for Session-Based Recommendation." Mathematics 9, no. 12 (2021): 1420. http://dx.doi.org/10.3390/math9121420.

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Session-based recommendation (SBRS) aims to make recommendations for users merely based on the ongoing session. Existing GNN-based methods achieve satisfactory performance by exploiting the pair-wise item transition pattern; however, they ignore the temporal evolution of the session graphs over different time-steps. Moreover, the widely applied cross-entropy loss with softmax in SBRS faces the serious overfitting problem. To deal with the above issues, we propose dynamic graph learning for session-based recommendation (DGL-SR). Specifically, we design a dynamic graph neural network (DGNN) to s

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Fanelli, Angelo, Laurent Gourvès, Ayumi Igarashi, and Luca Moscardelli. "Individually Stable Dynamics in Coalition Formation over Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 13 (2025): 13831–38. https://doi.org/10.1609/aaai.v39i13.33512.

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Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of stability, has attracted a lot of attention. However, the natural process by which players, starting from any feasible state, strive to reach an equilibrium after a series of unilateral improving deviations, has been less studied. We investigate the convergence of dynamics towards individually stable outcomes under the following perspective: what are the most genera

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Gustafson, Karl, and Robert Hartman. "Graph Theory and Fluid Dynamics." SIAM Journal on Algebraic Discrete Methods 6, no. 4 (1985): 643–56. http://dx.doi.org/10.1137/0606064.

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Collins, Pieter, and Kevin A. Mitchell. "Graph Duality in Surface Dynamics." Journal of Nonlinear Science 29, no. 5 (2019): 2103–35. http://dx.doi.org/10.1007/s00332-019-09549-0.

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Niehaus, Jens, Christian Igel, and Wolfgang Banzhaf. "Reducing the Number of Fitness Evaluations in Graph Genetic Programming Using a Canonical Graph Indexed Database." Evolutionary Computation 15, no. 2 (2007): 199–221. http://dx.doi.org/10.1162/evco.2007.15.2.199.

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In this paper we describe the genetic programming system GGP operating on graphs and introduce the notion of graph isomorphisms to explain how they influence the dynamics of GP. It is shown empirically how fitness databases can improve the performance of GP and how mapping graphs to a canonical form can increase these improvements by saving considerable evaluation time.

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