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1 International Journal of Applied Mathematics and Computer Science
1 Prace Naukowe Instytutu Technologii Organicznej i Tworzyw Sztucznych Politechniki Wrocławskiej. Konferencje

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Local dependency in networks

Kudělka M., Zehnalová Š., Horák Z., Krömer P., Snášel V.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 2

281--293

Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network's nodes from the structure in local surroundings of individual nodes. For the tasks we deal with in this article, the key technical parameter is locality. Since only the surroundings of the examined nodes are used in computations, there is no need to analyze the entire network. This allows the application of our approach in the area of large-scale networks. We present several experiments using small networks as well as large-scale artificial and real world networks. The results of the experiments show high effectiveness due to the locality of our approach and also high quality node ranking comparable to PageRank.

Equilibrium and non-equilibrium states in the compatibilization of PS/PB blends by means of styrene-butadiene block copolymers

Hlavatá D., Horák Z., Hromádková J.

Prace Naukowe Instytutu Technologii Organicznej i Tworzyw Sztucznych Politechniki Wrocławskiej. Konferencje

2001

Vol. 50, nr 23

327-330

Localization of styrene-butadiene block copolymers (BC) in both quenched and slowly cooled polystyrene (PS)/polybutadiene (PB) (4/1) blends was studied by means of small-angle X-ray scattering and transmission electron microscopy. Two types of BCs were used: (a) molecular weight of the styrene blocks is 10 000, i.e. below the critical molecular weight of styrene necessary for the entanglement formation (-18 000), (b) molecular weight of the styrene blocks is 40 000, i.e. it sufficiently exceeds this value. It has been shown that both types of the BCs used are in quickly cooled samples moleculary dispersed at the interface with an exception of 40S-60B-40S-60B-40S. In slowly cooled samples with addition of BCs with "short" styrene blocks, these BCs are released from the PS/PB interface, in contrast to the BCs having "long" styrene blocks.