scholarly journals Mining Preserving Structures in a Graph Sequence

2015 ◽  
pp. 3-15 ◽  
Author(s):  
Takeaki Uno ◽  
Yushi Uno
Keyword(s):  
Graph Sequence

scholarly journals Dynamic Planning of Bicycle Stations in Dockless Public Bicycle-sharing System Using Gated Graph Neural Network

2021 ◽  
Vol 12 (2) ◽  
pp. 1-22
Author(s):  
Jianguo Chen ◽  
Kenli Li ◽  
Keqin Li ◽  
Philip S. Yu ◽  
Zeng Zeng
Keyword(s):  
Large Scale ◽  
Sequence Data ◽  
Location Prediction ◽  
City Management ◽  
Dynamic Planning ◽  
Graph Sequence ◽  
Graph Modeling ◽  
The Government ◽  
Location Clustering ◽  
Station Location

Benefiting from convenient cycling and flexible parking locations, the Dockless Public Bicycle-sharing (DL-PBS) network becomes increasingly popular in many countries. However, redundant and low-utility stations waste public urban space and maintenance costs of DL-PBS vendors. In this article, we propose a Bicycle Station Dynamic Planning (BSDP) system to dynamically provide the optimal bicycle station layout for the DL-PBS network. The BSDP system contains four modules: bicycle drop-off location clustering, bicycle-station graph modeling, bicycle-station location prediction, and bicycle-station layout recommendation. In the bicycle drop-off location clustering module, candidate bicycle stations are clustered from each spatio-temporal subset of the large-scale cycling trajectory records. In the bicycle-station graph modeling module, a weighted digraph model is built based on the clustering results and inferior stations with low station revenue and utility are filtered. Then, graph models across time periods are combined to create a graph sequence model. In the bicycle-station location prediction module, the GGNN model is used to train the graph sequence data and dynamically predict bicycle stations in the next period. In the bicycle-station layout recommendation module, the predicted bicycle stations are fine-tuned according to the government urban management plan, which ensures that the recommended station layout is conducive to city management, vendor revenue, and user convenience. Experiments on actual DL-PBS networks verify the effectiveness, accuracy, and feasibility of the proposed BSDP system.

Out-of-equilibrium random walks

2020 ◽  
Vol 52 (3) ◽  
pp. 772-797
Author(s):  
Leonardo A. Videla
Keyword(s):  
Stochastic Process ◽  
Random Walks ◽  
Complete Graphs ◽  
Knowledge Process ◽  
Random Walker ◽  
Underlying Graph ◽  
Graph Sequence

AbstractWe study the long-term behaviour of a random walker embedded in a growing sequence of graphs. We define a (generally non-Markovian) real-valued stochastic process, called the knowledge process, that represents the ratio between the number of vertices already visited by the walker and the current size of the graph. We mainly focus on the case where the underlying graph sequence is the growing sequence of complete graphs.

Graphing Portfolios in Calculus: Reinforcing Concepts and Inviting Creativity

2005 ◽  
Vol 98 (6) ◽  
pp. 404-407
Author(s):  
Evelyn C. Bailey ◽  
Fang Chen
Keyword(s):  
Graph Sequence ◽  
Traditional Function

In this article, we introduce the idea of a graphing portfolio and describe its implementation in two levels of otherwise traditional university calculus courses. We believe that graphing portfolios facilitate learning because they require that students work backward from the traditional function to a graph sequence: To create a graphing portfolio, students must find functions whose graphs have specific shapes and domains. This process gives students the opportunity to investigate a variety of functions and transformations while incorporating their artistic and cultural strengths. The graphing portfolio is assigned after the class completes a unit on curve sketching as a way to apply concepts of calculus. We have found that this activity helps students gain a broader and deeper understanding of the connection between a function and its graph.

AMR Parsing via Graph-Sequence Iterative Inference

2020 ◽  
Author(s):  
Deng Cai ◽  
Wai Lam
Keyword(s):  
Graph Sequence

scholarly journals Convergence theorems for graph sequences

2014 ◽  
Vol 24 (08) ◽  
pp. 1233-1251 ◽  
Author(s):  
Felix Pogorzelski
Keyword(s):  
Banach Space ◽  
Integrated Density Of States ◽  
Finite Range ◽  
Amenable Groups ◽  
Finite Graphs ◽  
Graph Sequence ◽  
Discrete Structures ◽  
Long Term Behavior ◽  
Uniformly Bounded

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We examine their normalized long-term behavior along a particular class of graph sequences. Using techniques developed by Elek, we show convergence in the topology of the Banach space if the corresponding graph sequence possesses a hyperfinite structure. These considerations extend and complement the corresponding results for amenable groups. As an application, we verify the uniform approximation of the integrated density of states for bounded, finite range operators on discrete structures. Further, we extend results concerning an abstract version of Fekete's lemma for cancellative, amenable groups and semigroups to the geometric situation of convergent graph sequences.

Extraction of Community Transition Rules from Data Streams as Large Graph Sequence

2011 ◽  
Vol 15 (8) ◽  
pp. 1073-1081
Author(s):  
Takehiro Yamaguchi ◽  
◽  
Ayahiko Niimi ◽  
Keyword(s):  
Hierarchical Clustering ◽  
Data Streams ◽  
Graph Kernels ◽  
Large Graph ◽  
Relational Structures ◽  
Graph Sequence ◽  
Community Transition ◽  
Transition Rules ◽  
Synthetic Datasets ◽  
Social Bookmark

In this study, we treat transactional sets of data streams as a graph sequence. This graph sequence represents both the relational structures of data for each period and changes in these structures. In addition, we analyze changes in a community in this graph sequence. Our proposed algorithm extracts community transition rules to detect communities that appear irregularly in a graph sequence using our proposed method combined with adaptive graph kernels and hierarchical clustering. In experiments using synthetic datasets and social bookmark datasets, we demonstrate that our proposed algorithm detects changes in a community appearing irregularly.

Spectral Dynamics of Graph Sequences Generated by Subdivision and Triangle Extension

2017 ◽  
Vol 32 ◽  
pp. 454-463
Author(s):  
Haiyan Chen ◽  
Fuji Zhang
Keyword(s):  
Dynamic System ◽  
Closed Interval ◽  
Logistic Map ◽  
Quadratic Function ◽  
Spectral Dynamics ◽  
Laplacian Eigenvalues ◽  
Graph Sequence ◽  
Graph Operation ◽  
Limit Points ◽  
Trivial Graph

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].

scholarly journals Mobile Demand Forecasting via Deep Graph-Sequence Spatiotemporal Modeling in Cellular Networks

2018 ◽  
Vol 5 (4) ◽  
pp. 3091-3101 ◽  
Author(s):  
Luoyang Fang ◽  
Xiang Cheng ◽  
Haonan Wang ◽  
Liuqing Yang
Keyword(s):  
Cellular Networks ◽  
Demand Forecasting ◽  
Spatiotemporal Modeling ◽  
Graph Sequence
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