Analytically solvable processes on networks

@article{Smilkov2011AnalyticallySP,
  title={Analytically solvable processes on networks},
  author={Daniel Smilkov and Ljupco Kocarev},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2011},
  volume={84 1 Pt 2},
  pages={
          016104
        }
}
  • D. Smilkov, L. Kocarev
  • Published 11 March 2011
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and… 
1 Citations

Figures from this paper

Discrete-time distributed consensus on multiplex networks
We introduce a discrete-time distributed consensus process on multi-layered complex networks represented by multiplex graphs. The proposed consensus process can be characterized with a multiplex

References

SHOWING 1-10 OF 28 REFERENCES
Dynamical Processes on Complex Networks
TLDR
A new and recent account presents a comprehensive explanation of the effect of complex connectivity patterns on dynamical phenomena in a vast number of everyday systems that can be represented as large complex networks.
Finding community structure in very large networks.
TLDR
A hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure.
PageRank Computation, with Special Attention to Dangling Nodes
TLDR
A Jordan decomposition of the Google matrix for the (theoretical) extreme case when all Web pages are dangling nodes, when it is required to distinguish among different classes of dangling nodes.
Functional cartography of complex metabolic networks
TLDR
A methodology is proposed that can find functional modules in complex networks, and classify nodes into universal roles according to their pattern of intra- and inter-module connections, which yields a ‘cartographic representation’ of complex networks.
Cellular Automata Modeling of Physical Systems
  • B. Chopard
  • Computer Science
    Encyclopedia of Complexity and Systems Science
  • 2009
TLDR
Cellular automata modeling helps clarify the mechanics of lattice gas phenomena and provides insights into reaction-diffusion processes and their applications.
Problems in decentralized decision making and computation
TLDR
A scheme whereby a set of decision makers (processors) exchange and update tentative decisions which minimize a common cost function, given information they possess is considered; it is shown that they are guaranteed to converge to consensus.
Stochastic Processes and their Applications
Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some stochastic processes and their applications references. People with open
Diffusion and Reactions in Fractals and Disordered Systems
行 わ れ た 1段審査 を尊重 して 配分 した. 審査 の 印象 と して は次 の 点 が 挙げ られ る. 1) ボ ー ダ ー ラ イ ン で は 1段審査 員 の コ メ ン トが 必要で あ るが,それ に 欠 け る もの が 多 い. 2) 申請書 の 書 き方 と して ,2 段審査 委員 は も ち ろん ,点数をっ け る 1段 審査員 で も,決して 自分の 分野の 専
The PageRank Citation Ranking : Bringing Order to the Web
TLDR
This paper describes PageRank, a mathod for rating Web pages objectively and mechanically, effectively measuring the human interest and attention devoted to them, and shows how to efficiently compute PageRank for large numbers of pages.
Nature
  • R. Rosenfeld
  • Medicine
    Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery
  • 2009
...
...