Diffusion-Localization Transition Point of Gravity Type Transport Model on Regular Ring Lattices and Bethe Lattices

Koike, Hajime; Takayasu, Hideki; Takayasu, Misako

doi:10.1007/s10955-022-02882-x

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…As already described, we use the money transport model based on the gravity interaction model 18 , 19 , 33 for the sales estimation. The money flow defines the link direction, where a firm i buying (outflow) a product from a supplying firm j (inflow) is represented by the link , and the network representation as adjacency matrix is set to .…”

Section: Methodsmentioning

confidence: 99%

“…The money flow defines the link direction, where a firm i buying (outflow) a product from a supplying firm j (inflow) is represented by the link , and the network representation as adjacency matrix is set to . The original gravity interaction model 18 , 19 , 33 approximates that the total money flows out of a firm is proportional to the firm sales to the power of . It also indicates that the quota of the money flows to each trading partner is proportional to the partner’s sales to the power of .…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws

Ozaki,

Viegas,

Takayasu

et al. 2024

Sci Rep

Self Cite

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We develop a single two-layered model framework that captures and replicates both the statistical properties of the network as well as those of the intrinsic quantities of the agents. Our model framework consists of two distinct yet connected elements that were previously only studied in isolation, namely methods related to temporal network structures and those associated with money transport flows. Within this context, the network structure emerges from the first layer and its topological structure is transferred to the second layer associated with the money transactions. In this manner, we can explain how the micro-level dynamics of the agents within the network lead to the exogenous manifestation of the aggregated system statistical data en-wrapping the very same agents within the system. This is done by capturing the essential dynamics of collective motion in complex networks that enable the simultaneous emergence of tent-shaped distributions in growth rates within the agents, together with the emergence of scaling properties within the network in the study. We can validate the model framework and dynamics by applying these to the context of the real-world inter-firm trading network of firms in Japan and comparing the results of the statistical distributions at both network and agent levels in a temporal manner. In particular, we compare our results to the fundamental quantities supporting the seven empirical laws observed in data: the degree distribution, the mean degree growth rate over time, the age distribution of the firms, the preferential attachment, the sales distribution in steady states, their growth rates, their scaling relations generated by the model. We find these results to be nearly identical to the real-world data. The framework has the potential to be transformed into a forecasting tool to support decision-makers on financial and prudential policies.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws

Ozaki,

Viegas,

Takayasu

et al. 2024

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…As already described, we use the money transport model based on the gravity interaction model 19,24,25 for the sales estimation. The money flow defines the link direction, where a firm i buying (outflow) a product from a supplying firm j (inflow) is represented by the link i → j, and the network representation as adjacency matrix is set to A i j = 1.…”

Section: Model For Network Money Transport Layer (B)mentioning

confidence: 99%

“…The money flow defines the link direction, where a firm i buying (outflow) a product from a supplying firm j (inflow) is represented by the link i → j, and the network representation as adjacency matrix is set to A i j = 1. The original gravity interaction model 19,24,25 approximates that the total money flows out of a firm is proportional to the firm sales to the power of α ∼ 0.9. It also indicates that the quota of the money flows to each trading partner is proportional to the partner's sales to the power of β ∼ 0.3.…”

Section: Model For Network Money Transport Layer (B)mentioning

confidence: 99%

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws

Ozaki,

Viegas,

Takayasu

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

We develop a single two-layered model framework that captures and replicates both the statistical properties of the network as well as those of the intrinsic quantities of the agents. Our model framework consistently unifies two distinct yet interconnected elements that were previously only studied in isolation, namely methods related to temporal network structures and those associated with money transport flows. In this manner, we can explain how the micro-level dynamics of the agents within the network lead to the exogenous manifestation of the aggregated system statistical data en-wrapping the very same agents within the system. This is done by capturing the essential dynamics of collective motion in complex networks that enable the simultaneous emergence of tent-shaped distributions in growth rates within the agents, together with the emergence of scaling properties within the network in the study. We can validate the model framework and dynamics by applying these to the context of the real-world inter-firm trading network of firms in Japan and comparing the results of the statistical distributions at both network and agent levels in a temporal manner. In particular, we compare our results to the fundamental quantities supporting the seven empirical laws observed in data: the degree distribution, the mean degree growth rate over time, the age distribution of the firms, the preferential attachment, the sales distribution in steady states, their growth rates, their scaling relations generated by the model. We find these results to be nearly identical to the real-world data. The framework has the potential to be transformed into a forecasting tool to support decision-makers on financial and prudential policies.

show abstract

“…Another possible application concerns transportation networks, where the flux from one vertex to a connected one depends on some scalar quantities at the neighbouring vertices. This process is known as generalised gravity interaction and it gives rise to diffusion-localisation models on networks with nontrivial dynamics, see [32] and the references therein. We also mention social norm formation, [31], and biological transport networks, [1].…”

Section: Introductionmentioning

confidence: 99%

On evolution PDEs on co-evolving graphs

Esposito,

Mikolás

2024

DCDS

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We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the dynamics on the graph. This is relevant in applications to opinion dynamics and transportation networks. Existence and uniqueness of suitably defined solutions is obtained by exploiting the Banach fixed-point theorem. We consider different time scales for the evolution of the weight function: faster and slower than the flow defined on the graph. The former leads to graphs whose weight functions depend nonlocally on the density configuration at the vertices, while the latter induces static graphs. Furthermore, we prove a discrete-to-continuum limit for the PDEs under study as the number of vertices converges to infinity.

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Diffusion-Localization Transition Point of Gravity Type Transport Model on Regular Ring Lattices and Bethe Lattices

Cited by 4 publications

References 17 publications

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws

Integration of B-to-B trade network models of structural evolution and monetary flows reproducing all major empirical laws

On evolution PDEs on co-evolving graphs

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