Relevant bibliographies by topics / Graph dynamics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Graph dynamics'

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Published: 25 May 2024

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Journal articles on the topic "Graph dynamics"

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Huang, Xueqin, Xianqiang Zhu, Xiang Xu, Qianzhen Zhang, and Ailin Liang. "Parallel Learning of Dynamics in Complex Systems." Systems 10, no. 6 (December 15, 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 paper, the Dynamics-METIS (D-METIS) and the Partitioned Graph Neural Dynamics Learner (PGNDL). The general framework combines D-METIS and PGNDL to perform tasks for large graphs. D-METIS is a new algorithm that can partition a large graph into multiple subgraphs. D-METIS innovatively considers the dynamic changes in the graph. PGNDL is a new parallel model that consists of ordinary differential equation systems and graph neural networks (GNNs). It can quickly learn the dynamics of subgraphs in parallel. In this framework, D-METIS provides PGNDL with partitioned subgraphs, and PGNDL can solve the tasks of interpolation and extrapolation prediction. We exhibit the universality and superiority of our framework on four kinds of graphs with three kinds of dynamics through an experiment.
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Li, Jintang, Zhouxin Yu, Zulun Zhu, Liang Chen, Qi Yu, Zibin Zheng, Sheng Tian, Ruofan Wu, and Changhua Meng. "Scaling Up Dynamic Graph Representation Learning via Spiking Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 7 (June 26, 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 patterns of temporal graphs. We explore a new direction in that we can capture the evolving dynamics of temporal graphs with spiking neural networks (SNNs) instead of RNNs. As a low-power alternative to RNNs, SNNs explicitly model graph dynamics as spike trains of neuron populations and enable spike-based propagation in an efficient way. Experiments on three large real-world temporal graph datasets demonstrate that SpikeNet outperforms strong baselines on the temporal node classification task with lower computational costs. Particularly, SpikeNet generalizes to a large temporal graph (2.7M nodes and 13.9M edges) with significantly fewer parameters and computation overheads.
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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 (June 28, 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 for certain data while keeping the efficiency advantage of echo state networks. We show that AD-ESN can successfully discover the underlying pre-defined map- ping function and unknown nonlinear map-ping between time series and graphs.
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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 (October 30, 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 the cactus-path 〖Ch〗_(2,n) (composed of two same size ringsn). The upper bound is generalized on dynamic graphs based on cacti-paths with k rings. We show that for any constantly connected dynamic graph of size N based on a cactus-path, 4N -max{n_1,n_k} -3k -3 time units are sufficient to explore the graph, with k the length of the path, N=∑_(i=1)^k▒n_i -k+1 the size of the dynamic graph and n_i the size of the ring which is at position i starting from left to right.
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Di Ianni, Miriam. "Game of Life-like Opinion Dynamics: Generalizing the Underpopulation Rule." AppliedMath 3, no. 1 (December 28, 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 this paper, the generalization of the underpopulation rule to signed and directed graphs is studied. It is here proved that the number of label configurations met by a graph during the dynamic process defined by any so generalized underpopulation rule is still bounded by a polynomial in the size of the graph if the graph is undirected and structurally balanced, while it is not bounded by any polynomial in the size of the graph if the graph is directed although unsigned unless P = PSpace.
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Mouhamadou Wade, Ahmed. "EXPLORATION WITH RETURN OF HIGHLY DYNAMIC NETWORKS." International Journal of Advanced Research 9, no. 10 (October 31, 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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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 well-known logistic map; while that generated by triangle extension is determined by a linear function. By using the knowledge of dynamic system, the spectral dynamics of graph sequences generated by these two operations are characterized. For example, it is found that, for any initial non-trivial graph $G$, chaos takes place in the spectral dynamics of iterated subdivision graphs, and the set of limit points is the entire closed interval [0,2].
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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 (March 24, 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 differential equation, adeptly addressing the limitations of miscapturing signed information. Our proposed solution boasts both flexibility and efficiency. To substantiate its effectiveness, we seamlessly integrate our devised strategies into three preeminent graph-based dynamic modeling frameworks: graph neural ordinary differential equations, graph neural controlled differential equations, and graph recurrent neural networks. Rigorous assessments encompass three intricate dynamic scenarios from physics and biology, as well as scrutiny across four authentic real-world traffic datasets. Remarkably outperforming the trio of baselines, empirical results underscore the substantial performance enhancements facilitated by our proposed approach. Our code can be found at https://github.com/beautyonce/SGODE.
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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 (June 1, 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 of a wide range of large order solid continuum dynamics problems. With appropriate modifications, including the use of Eulerian (space fixed) bond graphs, the method may be extended to include fluid dynamics modeling.
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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 (November 9, 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 embeddings. On the other hand, the overall size of the network tends to accumulate over time, and its growth rate can reflect the ability of the entire network to generate interactions of heterogeneous nodes; therefore, we developed a graph dynamics model to model the evolution of graph dynamics. Moreover, the temporal properties of nodes regularly affect the generation of temporal interaction events with which they are connected. Thus, we developed a node dynamics model to model the evolution of node connectivity. In this paper, we propose DHGEEP, a dynamic heterogeneous graph-embedding method based on the Hawkes process, to predict the evolution of dynamic heterogeneous networks. The model considers the generation of temporal events as an effect of historical events, introduces the Hawkes process to simulate this evolution, and then captures semantic and structural information based on the meta-paths of temporal heterogeneous nodes. Finally, the graph-level dynamics of the network and the node-level dynamics of each node are integrated into the DHGEEP framework. The embeddings of the nodes are automatically obtained by minimizing the value of the loss function. Experiments were conducted on three downstream tasks, static link prediction, temporal event prediction for homogeneous nodes, and temporal event prediction for heterogeneous nodes, on three datasets. Experimental results show that DHGEEP achieves excellent performance in these tasks. In the most significant task, temporal event prediction of heterogeneous nodes, the values of precision@2 and recall@2 can reach 30.23% and 10.48% on the AMiner dataset, and reach 4.56% and 1.61% on the DBLP dataset, so that our method is more accurate at predicting future temporal events than the baseline.
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Dissertations / Theses on the topic "Graph dynamics"

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Ribeiro, Andre Figueiredo. "Graph dynamics : learning and representation." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34184.

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Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2006.
Includes bibliographical references (p. 58-60).
Graphs are often used in artificial intelligence as means for symbolic knowledge representation. A graph is nothing more than a collection of symbols connected to each other in some fashion. For example, in computer vision a graph with five nodes and some edges can represent a table - where nodes correspond to particular shape descriptors for legs and a top, and edges to particular spatial relations. As a framework for representation, graphs invite us to simplify and view the world as objects of pure structure whose properties are fixed in time, while the phenomena they are supposed to model are actually often changing. A node alone cannot represent a table leg, for example, because a table leg is not one structure (it can have many different shapes, colors, or it can be seen in many different settings, lighting conditions, etc.) Theories of knowledge representation have in general concentrated on the stability of symbols - on the fact that people often use properties that remain unchanged across different contexts to represent an object (in vision, these properties are called invariants). However, on closer inspection, objects are variable as well as stable. How are we to understand such problems? How is that assembling a large collection of changing components into a system results in something that is an altogether stable collection of parts?
(cont.) The work here presents one approach that we came to encompass by the phrase "graph dynamics". Roughly speaking, dynamical systems are systems with states that evolve over time according to some lawful "motion". In graph dynamics, states are graphical structures, corresponding to different hypothesis for representation, and motion is the correction or repair of an antecedent structure. The adapted structure is an end product on a path of test and repair. In this way, a graph is not an exact record of the environment but a malleable construct that is gradually tightened to fit the form it is to reproduce. In particular, we explore the concept of attractors for the graph dynamical system. In dynamical systems theory, attractor states are states into which the system settles with the passage of time, and in graph dynamics they correspond to graphical states with many repairs (states that can cope with many different contingencies). In parallel with introducing the basic mathematical framework for graph dynamics, we define a game for its control, its attractor states and a method to find the attractors. From these insights, we work out two new algorithms, one for Bayesian network discovery and one for active learning, which in combination we use to undertake the object recognition problem in computer vision. To conclude, we report competitive results in standard and custom-made object recognition datasets.
by Andre Figueiredo Ribeiro.
S.M.
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Kuhlman, Christopher James. "Generalizations of Threshold Graph Dynamical Systems." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/76765.

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Dynamics of social processes in populations, such as the spread of emotions, influence, language, mass movements, and warfare (often referred to individually and collectively as contagions), are increasingly studied because of their social, political, and economic impacts. Discrete dynamical systems (discrete in time and discrete in agent states) are often used to quantify contagion propagation in populations that are cast as graphs, where vertices represent agents and edges represent agent interactions. We refer to such formulations as graph dynamical systems. For social applications, threshold models are used extensively for agent state transition rules (i.e., for vertex functions). In its simplest form, each agent can be in one of two states (state 0 (1) means that an agent does not (does) possess a contagion), and an agent contracts a contagion if at least a threshold number of its distance-1 neighbors already possess it. The transition to state 0 is not permitted. In this study, we extend threshold models in three ways. First, we allow transitions to states 0 and 1, and we study the long-term dynamics of these bithreshold systems, wherein there are two distinct thresholds for each vertex; one governing each of the transitions to states 0 and 1. Second, we extend the model from a binary vertex state set to an arbitrary number r of states, and allow transitions between every pair of states. Third, we analyze a recent hierarchical model from the literature where inputs to vertex functions take into account subgraphs induced on the distance-1 neighbors of a vertex. We state, prove, and analyze conditions characterizing long-term dynamics of all of these models.
Master of Science
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Arnlind, Joakim. "Graph Techniques for Matrix Equations and Eigenvalue Dynamics." Doctoral thesis, KTH, Matematik (Inst.), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4608.

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One way to construct noncommutative analogues of a Riemannian manifold Σ is to make use of the Toeplitz quantization procedure. In Paper III and IV, we construct C-algebras for a continuously deformable class of spheres and tori, and by introducing the directed graph of a representation, we can completely characterize the representation theory of these algebras in terms of the corresponding graphs. It turns out that the irreducible representations are indexed by the periodic orbits and N-strings of an iterated map s:(reals) 2→(reals)2 associated to the algebra. As our construction allows for transitions between spheres and tori (passing through a singular surface), one easily sees how the structure of the matrices changes as the topology changes. In Paper II, noncommutative analogues of minimal surface and membrane equations are constructed and new solutions are presented -- some of which correspond to minimal tori embedded in S7. Paper I is concerned with the problem of finding differential equations for the eigenvalues of a symmetric N × N matrix satisfying Xdd=0. Namely, by finding N(N-1)/2 suitable conserved quantities, the time-evolution of X (with arbitrary initial conditions), is reduced to non-linear equations involving only the eigenvalues of Χ.
QC 20100630
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Ayazifar, Babak 1967. "Graph spectra and modal dynamics of oscillatory networks." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/16913.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2003.
Includes bibliographical references (leaves 186-191).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Our research focuses on developing design-oriented analytical tools that enable us to better understand how a network comprising dynamic and static elements behaves when it is set in oscillatory motion, and how the interconnection topology relates to the spectral properties of the system. Such oscillatory networks are ubiquitous, extending from miniature electronic circuits to large-scale power networks. We tap into the rich mathematical literature on graph spectra, and develop theoretical extensions applicable to networks containing nodes that have finite nonnegative weights-including nodes of zero weight, which occur naturally in the context of power networks. We develop new spectral graph-theoretic results spawned by our engineering interests, including generalizations (to node-weighted graphs) of various structure-based eigenvalue bounds. The central results of this thesis concern the phenomenon of dynamic coherency, in which clusters of vertices move in unison relative to each other. Our research exposes the relation between coherency and network structure and parameters. We study both approximate and exact dynamic coherency. Our new understanding of coherency leads to a number of results. We expose a conceptual link between theoretical coherency and the confinement of an oscillatory mode to a node cluster. We show how the eigenvalues of a coherent graph relate to those of its constituent clusters.
(cont.) We use our eigenvalue expressions to devise a novel graph design algorithm; given a set of vertices (of finite positive weight) and a desired set of eigenvalues, we construct a graph that meets the specifications. Our novel graph design algorithm has two interesting corollaries: the graph eigenvectors have regions of support that monotonically decrease toward faster modes, and we can construct graphs that exactly meet our generalized eigenvalue bounds. It is our hope that the results of this thesis will contribute to a better understanding of the links between structure and dynamics in oscillatory networks.
by Babak Ayazifar.
Ph.D.
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Homer, Martin Edward. "Bifurcations and dynamics of piecewise smooth dynamical systems of arbitrary dimension." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299271.

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Lee, Daryl Hsu Ann. "Toward large-graph comparison measures to understand Internet topology dynamics." Thesis, Monterey, California: Naval Postgraduate School, 2013. http://hdl.handle.net/10945/37658.

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By measuring network changes, we can get a better understanding of a network. Extending this to the Internet, we are able to understand the constantly occuring changes on an international scale. In this research, we propose a measure that conveys the relative magnitude of the change between two networks (i.e., Internet topology). The measure is normalised and intuitively gives an indication of whether the change is small or large. We start off by applying this measure to standard common graphs, as well as random graphs. These graphs were first simulated and the measurements taken; results were then proved theoretically. These corresponded to the simulation results, thus demonstrating correctness. For case studies, we compared actual implemented networks with that which is inferred by probes. This comparison was done to study how accurate the probes were in discovering actual network topology. Finally, we conducted real-world experiments by applying the measurements to certain segments of the Internet. We observed that the measurements indeed do pick up events which significantly influenced structural changes to the Internet.
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Giscard, Pierre-Louis. "A graph theoretic approach to matrix functions and quantum dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:ceef15b0-eed2-4615-a9f2-f9efbef470c9.

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Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.
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Ayala-Hoffmann, Jose. "Global behavior of graph dynamics with applications to Markov chains." [Ames, Iowa : Iowa State University], 2008.

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Magkakis, Andreas Gkompel. "Counting, modular counting and graph homomorphisms." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:42be90cd-75b5-43ec-ad2e-5d513420bdc0.

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A homomorphism from a graph G to a graph H is a function from V (G) to V (H) that preserves edges. Many combinatorial structures that arise in mathematics and in computer science can be represented naturally as graph homomorphisms and as weighted sums of graph homomorphisms. In this thesis we study the complexity of various problems related to graph homomorphisms.
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Budai, Daniel, and David Jallo. "The Market Graph : A study of its characteristics, structure & dynamics." Thesis, KTH, Matematisk statistik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-103094.

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In this thesis we have considered three different market graphs; one solely based on stock returns, another one based on stock returns with vertices weighted with a liquidity measure and lastly one based on correlations of volume fluctuations. Research is conducted on two different markets; the Swedish and the American stock market. We want to introduce graph theory as a method for representing the stock market in order to show that one can more fully understand the structural properties and dynamics of the stock market by studying the market graph. We found many signs of increased globalization by studying the clustering coefficient and the correlation distribution. The structure of the market graph is such that it pinpoints specific sectors when the correlation threshold is increased and different sectors are found in the two different markets. For low correlation thresholds we found groups of independent stocks that can be used as diversified portfolios. Furthermore, the dynamics revealed that it is possible to use the daily absolute change in edge density as an indicator for when the market is about to make a downturn. This could be an interesting topic for further studies. We had hoped to get additional results by considering volume correlations, but that did not turn out to be the case. Regardless of that, we think that it would be interesting to study volume based market graphs further.
I denna uppsats har vi tittat på tre olika marknadsgrafer; en enbart baserad på avkastning, en baserad på avkastning med likvidviktade noder och slutligen en baserad på volymkorrelationer. Studien är gjord på två olika marknader; den svenska och den amerikanska aktiemarknaden. Vi vill introducera grafteori som ett verktyg för att representera aktiemarknaden och visa att man bättre kan förstå aktiemarknadens strukturerade egenskaper och dynamik genom att studera marknadsgrafen. Vi fann många tecken på en ökad globalisering genom att titta på klusterkoefficienten och korrelationsfördelningen. Marknadsgrafens struktur är så att den lokaliserar specifika sektorer när korrelationstaket ökas och olika sektorer är funna för de två olika marknaderna. För låga korrelationstak fann vi grupper av oberoende aktier som kan användas som diversifierade portföljer. Vidare, avslöjar dynamiken att det är möjligt att använda daglig absolut förändring i bågdensiteten som en indikator för när marknaden är på väg att gå ner. Detta kan vara ett intressant ämne för vidare studier. Vi hade hoppats på att erhålla ytterligare resultat genom att titta på volymkorrelationer men det visade sig att så inte var fallet. Trots det tycker vi att det skulle vara intressant att djupare studera volymbaserade marknadsgrafer.
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Books on the topic "Graph dynamics"

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Prisner, E. Graph dynamics. New York: Longman, 1995.

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Prisner, E. Graph dynamics. Harlow, Essex: Longman, 1995.

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Random graph dynamics. Cambridge: Cambridge University Press, 2007.

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Świder, Jerzy. Macierzowe grafy hybrydowe w opisie drgających, złożonych układów mechanicznych. Gliwice: Wydawn. Politechniki Śląskiej, 1991.

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Brown, Forbes T. Engineering system dynamics: A unified graph-centered approach. 2nd ed. Boca Raton, FL: CRC/Taylor & Francis, 2006.

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Engineering system dynamics: A unified graph-centered approach. New York: Marcel Dekker, 2001.

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Horst, Bunke, ed. A graph-theoretic approach to enterprise network dynamics. Boston: Birkhäuser, 2007.

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Mariusz, Urbaʹnski, ed. Graph directed Markov systems: Geometry and dynamics of limit sets. Cambridge: Cambridge University Press, 2003.

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Watts, Duncan J. Small worlds: The dynamics of networks between order and randomness. Princeton, N.J: Princeton University Press, 1999.

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Osipenko, Georgiy. Computer-oriented methods of dynamic systems. ru: INFRA-M Academic Publishing LLC., 2023. http://dx.doi.org/10.12737/1912470.

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The methods of studying the global properties of dynamic systems based on the construction of a symbolic image of this system are considered. A symbolic image is an oriented graph, which is an approximation to a dynamical system and is constructed by discretizing the phase space. The symbolic dynamics generated by the oriented graph reflects the dynamics of the system under study. The symbolic image is a tool of theoretical research and the basis of computer-oriented methods for the numerical study of nonlocal properties of dynamical systems. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in the field of Applied Mathematics and Computer Science. It will be useful for graduate students and researchers studying dynamical systems and their applications.
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Book chapters on the topic "Graph dynamics"

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Arrighi, Pablo, and Gilles Dowek. "Causal Graph Dynamics." In Automata, Languages, and Programming, 54–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31585-5_9.

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Cittadini, Luca, Tiziana Refice, Alessio Campisano, Giuseppe Di Battista, and Claudio Sasso. "Policy-Aware Visualization of Internet Dynamics." In Graph Drawing, 435–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00219-9_43.

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Jain, Abhinandan. "Graph Theory Connections." In Robot and Multibody Dynamics, 135–57. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-7267-5_8.

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Fagnani, Fabio, and Paolo Frasca. "Graph Theory." In Introduction to Averaging Dynamics over Networks, 1–30. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68022-4_1.

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King, R. B. "Polyhedral Dynamics." In Graph Theoretical Approaches to Chemical Reactivity, 109–35. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1202-4_4.

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Arrighi, Pablo, Simon Martiel, and Simon Perdrix. "Reversible Causal Graph Dynamics." In Reversible Computation, 73–88. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40578-0_5.

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van Benthem, Johan, and Fenrong Liu. "Graph Games and Logic Design." In Knowledge, Proof and Dynamics, 125–46. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2221-5_7.

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Seeler, Karl A. "Introduction to the Linear Graph Method, Step Responses, and Superposition." In System Dynamics, 117–93. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-9152-1_3.

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Dell’Antonio, Gianfausto, and Alessandro Michelangeli. "Dynamics on a Graph as the Limit of the Dynamics on a “Fat Graph”." In Mathematical Technology of Networks, 49–64. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16619-3_5.

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Jacob, Abraham, and P. B. Ramkumar. "Intuitionistic Fuzzy Graph Morphological Topology." In Topological Dynamics and Topological Data Analysis, 255–62. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0174-3_21.

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Conference papers on the topic "Graph dynamics"

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Belim, Sergey V., and Anton N. Mironenko. "Using the graph-theoretic approach to solving the Role Mining problem." In 2018 Dynamics of Systems, Mechanisms and Machines (Dynamics). IEEE, 2018. http://dx.doi.org/10.1109/dynamics.2018.8601487.

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Cai, Borui, Yong Xiang, Longxiang Gao, He Zhang, Yunfeng Li, and Jianxin Li. "Temporal Knowledge Graph Completion: A Survey." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/734.

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Knowledge graph completion (KGC) predicts missing links and is crucial for real-life knowledge graphs, which widely suffer from incompleteness. KGC methods assume a knowledge graph is static, but that may lead to inaccurate prediction results because many facts in the knowledge graphs change over time. Emerging methods have recently shown improved prediction results by further incorporating the temporal validity of facts; namely, temporal knowledge graph completion (TKGC). With this temporal information, TKGC methods explicitly learn the dynamic evolution of the knowledge graph that KGC methods fail to capture. In this paper, for the first time, we comprehensively summarize the recent advances in TKGC research. First, we detail the background of TKGC, including the preliminary knowledge, benchmark datasets, and evaluation metrics. Then, we summarize existing TKGC methods based on how the temporal validity of facts is used to capture the temporal dynamics. Finally, we conclude the paper and present future research directions of TKGC.
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Lesfari, Hicham, Frédéric Giroire, and Stéphane Pérennes. "Biased Majority Opinion Dynamics: Exploiting Graph k-domination." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/54.

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We study opinion dynamics in multi-agent networks where agents hold binary opinions and are influenced by their neighbors while being biased towards one of the two opinions, called the superior opinion. The dynamics is modeled by the following process: at each round, a randomly selected agent chooses the superior opinion with some probability α, and with probability 1-α it conforms to the opinion manifested by the majority of its neighbors. In this work, we exhibit classes of network topologies for which we prove that the expected time for consensus on the superior opinion can be exponential. This answers an open conjecture in the literature. In contrast, we show that in all cubic graphs, convergence occurs after a polynomial number of rounds for every α. We rely on new structural graph properties by characterizing the opinion formation in terms of multiple domination, stable and decreasing structures in graphs, providing an interplay between bias, consensus and network structure. Finally, we provide both theoretical and experimental evidence for the existence of decreasing structures and relate it to the rich behavior observed on the expected convergence time of the opinion diffusion model.
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Mancini, Felice, Daniel Grande, and Pradeep Radhakrishnan. "An Automated Virtual Lab for Bond Graph Based Dynamics Modeling Using Graph Grammars and Tree Search." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66110.

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This paper explores the concept of an automated virtual lab in the area of system design and analysis. The project combines different research activities in automated design analysis using the graph grammar and tree search methods. In particular, a graph grammar rule-based system to automatically generate bond graphs for various systems is developed. This is combined with similar grammar based rules and search algorithms to provide automation as well as context sensitive feedback to users of the virtual lab. Examples will be demonstrated to showcase the potential as well as how the virtual lab can be scaled using appropriate learning algorithms towards personalizing education.
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Grande, Daniel, Felice Mancini, and Pradeep Radhakrishnan. "An Automated Graph Grammar Based Tool to Automatically Generate System Bond Graphs for Dynamic Analysis." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59941.

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This paper presents a graph grammar based automated tool that can generate bond graphs of various systems for dynamic analysis. A generic graph grammar based representation scheme has been developed for different system components and bond graph elements. Using that representation, grammar rules have been developed that enable interpreting a given system and generating bond graph through an algorithmic search process. Besides, the paper also demonstrates the utility of the proposed tool in classrooms to enhance value in bond graph based system dynamics education. The underlying technique, various examples and benefits of this automated tool will be highlighted.
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Yin, Cheng, Shengqi Jian, Md Hassan Faghih, Md Toufiqul Islam, and Luc Rolland. "Bond Graph Modeling and Simulating of 3 RPR Planar Parallel Manipulator." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38601.

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A 3-RPR planar parallel robot is a kind of planar mechanisms, which can work at high speed, with high accuracy and high rigidity. In this paper, a multi-body bond graph system will be built for the 3-RPR planar parallel manipulator (PPM), along with 3 PID controllers which give commands to 3 DC motors respectively. The advantage of bond graphs is that they can integrate different types of dynamics systems, the manipulator, the control and the motor can be modelled and simulated altogether in the same process. Bond graph will be established for each rigid body with body-fixed coordinate’s reference frames, which are connected with parasitic elements (damping and compliance) to each other. The PID set-point signals are generated by the explicit inverse kinematic equations. The 3 prismatic lengths constitute the measured feedback signals. In order to make the end-effector reach the ideal position with target orientation, the three links should reach the target lengths simultaneously. In this study, the dynamics simulation of 3-RPR PPM is conducted after building the bond graph system. As the 3 motors are working simultaneously and independently, the end-effector will arrive to the expected position. Finally, the bond graph and control system are validated with the compiled results and 3D animation. Force plot and torque plot will be generated as dynamics performance. Moreover, kinematics of manipulators are also calculated using bond graph. Eventually, bond graphs are shown to be effective in solving not only dynamic but also kinematic problems.
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Popov, Anton I., Igor Y. Popov, Dmitri S. Nikiforov, and Irina V. Blinova. "Time-dependent metric graph: Wave dynamics." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114299.

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Burch, Michael, Günter Wallner, Huub van de Wetering, Freek Rooks, and Olof Morra. "Visual Analysis of Graph Algorithm Dynamics." In VINCI 2021: The 14th International Symposium on Visual Information Communication and Interaction. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3481549.3481550.

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Wu, Zhaohong, Matthew I. Campbell, and Benito R. Fernandez. "A Design Representation to Support the Automatic Dynamic Evaluation of Electromechanical Designs." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81799.

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This paper introduces research leading to a computer-aided design tool in which engineering designers can test various concepts in an environment equipped to automatically model the dynamics and then optimize the chosen components to best meet the specifications of the design problem. The input to the system is a graph of components where the components either include defined parameter values or are left as variables for the subsequent optimization. In this paper, “conceptual dynamics” is introduced with the goal of revealing the qualitative information of the system states, energy flow patterns, possible operation modes, degrees of freedom, etc. The dynamics of a system are captured in a multi-domain representation referred to as a conceptual dynamics graph (CD-Graph), which is composed of components and virtual couplers. The components feature both detailed multi-complexity models (bond graphs) and qualitative dynamics information (Conceptual Dynamics Matrices), and the virtual couplers include information on the interconnections of the eight domains (three translational, three rotational, electrical, and hydraulic). The Conceptual Dynamics Graph provides a platform for various design automation approaches and further dynamics performance optimization. This paper discusses an automatic approach that extracts the partial configuration of a complete design structure that contributes to the system dynamics. This allows designers to better understand the system and focus on the functional aspects that meet certain dynamic specifications. Finally an automatic model generation approach of CD-Graph is briefly illustrated.
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Sharma, Kartik, Rakshit Trivedi, Rohit Sridhar, and Srijan Kumar. "Temporal Dynamics-Aware Adversarial Attacks on Discrete-Time Dynamic Graph Models." In KDD '23: The 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2023. http://dx.doi.org/10.1145/3580305.3599517.

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Reports on the topic "Graph dynamics"

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Djidjev, Hristo Nikolov, Georg Hahn, Susan M. Mniszewski, Christian Francisco Negre, Anders Mauritz Niklasson, and Vivek Sardeshmukh. Graph Partitioning Methods for Fast Parallel Quantum Molecular Dynamics. Office of Scientific and Technical Information (OSTI), October 2016. http://dx.doi.org/10.2172/1330079.

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Thulasidasan, Sunil. The Graph Laplacian and the Dynamics of Complex Networks. Office of Scientific and Technical Information (OSTI), June 2012. http://dx.doi.org/10.2172/1043504.

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Chew, Geoffrey F. Quantum dynamics via Planck-scale-stepped action-carrying 'Graph Paths'. Office of Scientific and Technical Information (OSTI), May 2003. http://dx.doi.org/10.2172/813522.

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Kularatne, Dhanushka N., Subhrajit Bhattacharya, and M. Ani Hsieh. Computing Energy Optimal Paths in Time-Varying Flows. Drexel University, 2016. http://dx.doi.org/10.17918/d8b66v.

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Autonomous marine vehicles (AMVs) are typically deployed for long periods of time in the ocean to monitor different physical, chemical, and biological processes. Given their limited energy budgets, it makes sense to consider motion plans that leverage the dynamics of the surrounding flow field so as to minimize energy usage for these vehicles. In this paper, we present two graph search based methods to compute energy optimal paths for AMVs in two-dimensional (2-D) time-varying flows. The novelty of the proposed algorithms lies in a unique discrete graph representation of the 3-D configuration space spanned by the spatio-temporal coordinates. This enables a more efficient traversal through the search space, as opposed to a full search of the spatio-temporal configuration space. Furthermore, the proposed strategy results in solutions that are closer to the global optimal when compared to greedy searches through the spatial coordinates alone. We demonstrate the proposed algorithms by computing optimal energy paths around the Channel Islands in the Santa Barbara bay using time-varying flow field forecasts generated by the Regional Ocean Model System. We verify the accuracy of the computed paths by comparing them with paths computed via an optimal control formulation.
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Mesbahi, Mehran. Dynamic Security and Robustness of Networked Systems: Random Graphs, Algebraic Graph Theory, and Control over Networks. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567125.

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Soloviev, Vladimir, Victoria Solovieva, Anna Tuliakova, Alexey Hostryk, and Lukáš Pichl. Complex networks theory and precursors of financial crashes. [б. в.], October 2020. http://dx.doi.org/10.31812/123456789/4119.

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Based on the network paradigm of complexity in the work, a systematic analysis of the dynamics of the largest stock markets in the world and cryptocurrency market has been carried out. According to the algorithms of the visibility graph and recurrence plot, the daily values of stock and crypto indices are converted into a networks and multiplex networks, the spectral and topological properties of which are sensitive to the critical and crisis phenomena of the studied complex systems. This work is the first to investigate the network properties of the crypto index CCI30 and the multiplex network of key cryptocurrencies. It is shown that some of the spectral and topological characteristics can serve as measures of the complexity of the stock and crypto market, and their specific behaviour in the pre-crisis period is used as indicators- precursors of critical phenomena.
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Gallagher, B., and T. Eliassi-Rad. API Requirements for Dynamic Graph Prediction. Office of Scientific and Technical Information (OSTI), October 2006. http://dx.doi.org/10.2172/1036864.

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Khanna, S., R. Motwani, and R. H. Wilson. On certificates and lookahead in dynamic graph problems. Office of Scientific and Technical Information (OSTI), May 1995. http://dx.doi.org/10.2172/93769.

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Bhatele, Abhinav, Sebastien Fourestier, Harshitha Menon, Laxmikant V. Kale, and Francois Pellegrini. Applying graph partitioning methods in measurement-based dynamic load balancing. Office of Scientific and Technical Information (OSTI), September 2011. http://dx.doi.org/10.2172/1114706.

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Labute, M., and M. Dombroski. Review of Graph Databases for Big Data Dynamic Entity Scoring. Office of Scientific and Technical Information (OSTI), May 2014. http://dx.doi.org/10.2172/1132027.

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