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Search Results: 1 - 10 of 2608 matches for " Krzysztof Suchecki "
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Hierarchy depth in directed networks
Krzysztof Suchecki,Janusz Holyst
Physics , 2013,
Abstract: We explore depth measures for flow hierarchy in directed networks. We define two measures -- rooted depth and relative depth, and discuss differences between them. We investigate how the two measures behave in random Erdos-Renyi graphs of different sizes and densities and explain obtained results.
First order phase transition in Ising model on two connected Barabasi-Albert networks
Krzysztof Suchecki,Janusz A. Holyst
Physics , 2008,
Abstract: We investigate the behavior of the Ising model on two connected Barabasi-Albert scale-free networks. We extend previous analysis and show that a first order temperature-driven phase transition occurs in such system. The transition between antiparalelly ordered networks to paralelly ordered networks is shown to be discontinuous. We calculate the critical temperature. We confirm the calculations with numeric simulations using Monte-Carlo methods.
Voter model on Sierpinski fractals
Krzysztof Suchecki,Janusz A. Holyst
Physics , 2005, DOI: 10.1016/j.physa.2005.08.003
Abstract: We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification.
Log-periodic oscillations in degree distributions of hierarchical scale-free networks
Krzysztof Suchecki,Janusz A. Holyst
Physics , 2005,
Abstract: Hierarchical models of scale free networks are introduced where numbers of nodes in clusters of a given hierarchy are stochastic variables. Our models show periodic oscillations of degree distribution P(k) in the log-log scale. Periods and amplitudes of such oscillations depend on network parameters. Numerical simulations are in a good agreement to analytical calculations.
Ising model on two connected Barabasi-Albert networks
Krzysztof Suchecki,Janusz A. Holyst
Physics , 2006, DOI: 10.1103/PhysRevE.74.011122
Abstract: We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.
Highly connected - a recipe for success
Krzysztof Suchecki,Andrea Scharnhorst,Janusz A. Holyst
Physics , 2010,
Abstract: In this paper, we tackle the problem of innovation spreading from a modeling point of view. We consider a networked system of individuals, with a competition between two groups. We show its relation to the innovation spreading issues. We introduce an abstract model and show how it can be interpreted in this framework, as well as what conclusions we can draw form it. We further explain how model-derived conclusions can help to investigate the original problem, as well as other, similar problems. The model is an agent-based model assuming simple binary attributes of those agents. It uses a majority dynamics (Ising model to be exact), meaning that individuals attempt to be similar to the majority of their peers, barring the occasional purely individual decisions that are modeled as random. We show that this simplistic model can be related to the decision-making during innovation adoption processes. The majority dynamics for the model mean that when a dominant attribute, representing an existing practice or solution, is already established, it will persists in the system. We show however, that in a two group competition, a smaller group that represents innovation users can still convince the larger group, if it has high self-support. We argue that this conclusion, while drawn from a simple model, can be applied to real cases of innovation spreading. We also show that the model could be interpreted in different ways, allowing different problems to profit from our conclusions.
Hierarchical Cont-Bouchaud model
Robert Paluch,Krzysztof Suchecki,Janusz A. Holyst
Physics , 2015,
Abstract: We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdos-Renyi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdos-Renyi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.
Models of random graph hierarchies
Robert Paluch,Krzysztof Suchecki,Janusz Holyst
Computer Science , 2015,
Abstract: We introduce two models of inclusion hierarchies: Random Graph Hierarchy (RGH) and Limited Random Graph Hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erd\H{o}s-R\'{e}nyi random graph, with a fixed average degree equal to a system parameter $c$. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size $1$, when building the next hierarchy level, while in the LRGH model clusters of size $1$ stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level $h$ decreases approximately exponentially with $h$. The height of the hierarchy $H$, i.e. the number of all hierarchy levels, increases logarithmically with the system size $N$, i.e. with the number of nodes at the first level. The height $H$ decreases monotonically with the connectivity parameter $c$ in the RGH model and it reaches a maximum for a certain $c_{max}$ in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about $-1.25$. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.
Networks of companies and branches in Poland
Anna M. Chmiel,Julian Sienkiewicz,Krzysztof Suchecki,Janusz A. Holyst
Physics , 2006, DOI: 10.1016/j.physa.2007.04.095
Abstract: In this study we consider relations between companies in Poland taking into account common branches they belong to. It is clear that companies belonging to the same branch compete for similar customers, so the market induces correlations between them. On the other hand two branches can be related by companies acting in both of them. To remove weak, accidental links we shall use a concept of threshold filtering for weighted networks where a link weight corresponds to a number of existing connections (common companies or branches) between a pair of nodes.
Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
Krzysztof Suchecki,Víctor M. Eguíluz,Maxi San Miguel
Physics , 2005, DOI: 10.1103/PhysRevE.72.036132
Abstract: We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find that when there is no ordering in the system, the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity. The existence of hubs in the network modifies the linear system size scaling law of the survival time. The size of an ordered domain is sensitive to the network disorder and the average connectivity, decreasing with both; however it seems not to depend on network size and degree heterogeneity.
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