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Relevant bibliographies by topics / Parametrized graphs

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Journal articles

Academic literature on the topic 'Parametrized graphs'

Author: Grafiati

Published: 4 April 2023

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Journal articles on the topic "Parametrized graphs"

1

Faran, Rachel, and Orna Kupferman. "A Parametrized Analysis of Algorithms on Hierarchical Graphs." International Journal of Foundations of Computer Science 30, no. 06n07 (2019): 979–1003. http://dx.doi.org/10.1142/s0129054119400252.

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Hierarchical graphs are used in order to describe systems with a sequential composition of sub-systems. A hierarchical graph consists of a vector of subgraphs. Vertices in a subgraph may “call” other subgraphs. The reuse of subgraphs, possibly in a nested way, causes hierarchical graphs to be exponentially more succinct than equivalent flat graphs. Early research on hierarchical graphs and the computational price of their succinctness suggests that there is no strong correlation between the complexity of problems when applied to flat graphs and their complexity in the hierarchical setting. That is, the complexity in the hierarchical setting is higher, but all “jumps” in complexity up to an exponential one are exhibited, including no jumps in some problems. We continue the study of the complexity of algorithms for hierarchical graphs, with the following contributions: (1) In many applications, the subgraphs have a small, often a constant, number of exit vertices, namely vertices from which control returns to the calling subgraph. We offer a parameterized analysis of the complexity and point to problems where the complexity becomes lower when the number of exit vertices is bounded by a constant. (2) We describe a general methodology for algorithms on hierarchical graphs. The methodology is based on an iterative compression of subgraphs in a way that maintains the solution to the problems and results in subgraphs whose size depends only on the number of exit vertices, and (3) we handle labeled hierarchical graphs, where edges are labeled by letters from some alphabet, and the problems refer to the languages of the graphs.

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2

ELLIS-MONAGHAN, JOANNA A., and LORENZO TRALDI. "Parametrized Tutte Polynomials of Graphs and Matroids." Combinatorics, Probability and Computing 15, no. 06 (2006): 835. http://dx.doi.org/10.1017/s0963548306007656.

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3

Asaeda, Marta, and Uffe Haagerup. "Fusion rules on a parametrized series of graphs." Pacific Journal of Mathematics 253, no. 2 (2011): 257–88. http://dx.doi.org/10.2140/pjm.2011.253.257.

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4

Sadeghian, Ali, Mohammadreza Armandpour, Anthony Colas, and Daisy Zhe Wang. "ChronoR: Rotation Based Temporal Knowledge Graph Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (2021): 6471–79. http://dx.doi.org/10.1609/aaai.v35i7.16802.

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Despite the importance and abundance of temporal knowledge graphs, most of the current research has been focused on reasoning on static graphs. In this paper, we study the challenging problem of inference over temporal knowledge graphs. In particular, the task of temporal link prediction. In general, this is a difficult task due to data non-stationarity, data heterogeneity, and its complex temporal dependencies. We propose Chronological Rotation embedding (ChronoR), a novel model for learning representations for entities, relations, and time. Learning dense representations is frequently used as an efficient and versatile method to perform reasoning on knowledge graphs. The proposed model learns a k-dimensional rotation transformation parametrized by relation and time, such that after each fact's head entity is transformed using the rotation, it falls near its corresponding tail entity. By using high dimensional rotation as its transformation operator, ChronoR captures rich interaction between the temporal and multi-relational characteristics of a Temporal Knowledge Graph. Experimentally, we show that ChronoR is able to outperform many of the state-of-the-art methods on the benchmark datasets for temporal knowledge graph link prediction.

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5

Keros, Alexandros D., Vidit Nanda, and Kartic Subr. "Dist2Cycle: A Simplicial Neural Network for Homology Localization." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (2022): 7133–42. http://dx.doi.org/10.1609/aaai.v36i7.20673.

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Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher dimensional topological features of data, features to which graphs, encoding only pairwise relationships, remain oblivious. While attempts have been made to extend Graph Neural Networks (GNNs) to a simplicial complex setting, the methods do not inherently exploit, or reason about, the underlying topological structure of the network. We propose a graph convolutional model for learning functions parametrized by the k-homological features of simplicial complexes. By spectrally manipulating their combinatorial k-dimensional Hodge Laplacians, the proposed model enables learning topological features of the underlying simplicial complexes, specifically, the distance of each k-simplex from the nearest "optimal" k-th homology generator, effectively providing an alternative to homology localization.

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6

LEFLOCH, PHILIPPE G. "GRAPH SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS." Journal of Hyperbolic Differential Equations 01, no. 04 (2004): 643–89. http://dx.doi.org/10.1142/s0219891604000287.

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For nonlinear hyperbolic systems of partial differential equations in one-space dimension (in either conservative or non-conservative form) we introduce a geometric framework in which solutions are sought as (continuous) parametrized graphs(t,s) ↦ (X,U)(t,s) satisfying ∂sX ≥ 0, rather than (discontinuous) functions (t,x) ↦ u(t,x). On one hand, we generalize an idea by Dal Maso, LeFloch, and Murat who used a family of traveling wave profiles to define non-conservative products, and we define the notion of graph solution subordinate to a family of Riemann graphs. The latter naturally encodes the graph of the solution to the Riemann problem, which should be determined from an augmented model taking into account small-scale physics and providing an internal structure to the shock waves. In a second definition, we write an evolution equation on the graphs directly and we introduce the notion of graph solution subordinate to a diffusion matrix, which merges together the hyperbolic equations (in the "non-vertical" parts of the graphs) with the traveling wave equation of the augmented model (in the "vertical" parts). We consider the Cauchy problem within the class of graph solutions. The graph solution to the Cauchy problem is constructed by completion of the discontinuities of the entropy solution. The uniqueness is established by applying a general uniqueness theorem due to Baiti, LeFloch, and Piccoli. The proposed geometric framework illustrates the importance of the uniform distance between graphs to deal with solutions of nonlinear hyperbolic problems.

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7

Hussein, Amru. "Sign-indefinite second-order differential operators on finite metric graphs." Reviews in Mathematical Physics 26, no. 04 (2014): 1430003. http://dx.doi.org/10.1142/s0129055x14300039.

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The question of self-adjoint realizations of sign-indefinite second-order differential operators is discussed in terms of a model problem. Operators of the type [Formula: see text] are generalized to finite, not necessarily compact, metric graphs. All self-adjoint realizations are parametrized using methods from extension theory. The spectral and scattering theories of the self-adjoint realizations are studied in detail.

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8

Aristoff, David, and Lingjiong Zhu. "On the phase transition curve in a directed exponential random graph model." Advances in Applied Probability 50, no. 01 (2018): 272–301. http://dx.doi.org/10.1017/apr.2018.13.

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Abstract We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and, in particular, an appropriately scaled limit of the normalization, which is called the free energy. We derive precise asymptotics for the normalization constant for finite graphs. We use this to derive a formula for the free energy. The limit is analytic everywhere except along a curve corresponding to a first-order phase transition. We examine unusual behavior of the model along the phase transition curve.

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9

Stefanou, Anastasios. "Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics." Journal of Applied and Computational Topology 4, no. 2 (2020): 281–308. http://dx.doi.org/10.1007/s41468-020-00051-1.

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10

Galvez, Carmen, and Félix Moya-Anegón. "The unification of institutional addresses applying parametrized finite-state graphs (P-FSG)." Scientometrics 69, no. 2 (2006): 323–45. http://dx.doi.org/10.1007/s11192-006-0156-3.

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