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A comparative performance analysis of the exponential-based and resolvent-based centrality measures

Wilczek Piotr

Silesian Journal of Pure and Applied Mathematics

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2020

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vol. 10, iss. 1

45--102

EN

The present study aims to quantitatively assess the effect of the attenuation factor on the resolution, performance, rank correlations, robustness and assortativity of the Katz centrality measure. We found that the granularity of the exponential-based and resolvent-based ranking algorithms is strongly correlated with the number of automorphically equivalent nodes within the network. Thus, this result can be viewed as a bridge between algebraic and quantitative graph theory. Moreover, we substituted the dichotomous adjacency matrix in the definitions of the exponential-based and resolvent-based centrality indices by its weighted (normalized) version and, therefore, we obtained two novel ranking algorithms. The deliberate attack simulation experiments carried out on four empirical and on two model networks showcased that the newly suggested ranking methods considerably outperform their unweighted counterparts as well as the classical degree centrality measure. In the last part of the paper, we introduced the concept of the centrality assortativity profile of a complex network. The extensive numerical results demonstrated that this novel theoretical notion is useful in complex network mining.

2

The interaction of laser radiation with tissue in the aspect of generating the process of decellularization in the preparation of animal origin autologous tissue

Kopernik Magdalena, Major Roman, Lis Grzegorz, Wilczek Piotr, Lis Maciej, Imbir Gabriela, Chrouda Abir, Mzyk Aldona, Ostrowski Roman, Sanak Marek

Acta of Bioengineering and Biomechanics

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2020

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Vol. 22, no. 1

67--77

EN

Purpose: The aim of the work was to create an appropriate substrate for organ transplantation using bioactive tissue-based scaffold populated by cells of the graft recipient. The purpose of the modeling was to investigate the mechanical effects of wave loading of aortic and pulmonary tissue material. Methods: The biological properties of tissues of aortic and pulmonary valves were modified by the process of decellularization. The host cells were removed by various physical methods with focus on minimal degradation of the extracellular matrix. Thus, the decellularization process was controlled by histological methods. The tissue decellularization process was simulated by finite element modelling. Results: The mechanical results represented by a displacement at the center of the sample were coherent and the heterogeneity of the distribution of the caves on the surface of the samples was confirmed, both by experiment and in the simulation by the alternate occurrence of local minima and maxima. The latter results from the uneven removal of cells from the effect of the wave causing decellularization were also predicted by the numerical model. Laser radiation had a destructive effect on the components of the extracellular matrix (e.g., collagen and elastic fibers), mainly depending on the fluence and number of pulses in a single exposure. Conclusions: The differences between the valve tissue materials were shown, and the impact of the process of decellularization on the properties of the tissues was analyzed. It should be emphasized that due to low absorption and high scattering, laser radiation can deeply penetrate the tissue, which allows for effective decellularization process in the entire volume of irradiated tissue.

3

Identifying influential nodes in the genome-scale metabolic networks

Wilczek Piotr

Silesian Journal of Pure and Applied Mathematics

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2019

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vol. 9, iss. 1

9--47

EN

The present article introduces two novel centrality indices which can be used in order to characterize the genome-scale metabolic networks. The deliberate attack simulation experiments conducted on two Barab´asi-Albert models and four genome-scale metabolic networks demonstrate that the proposed ranking methods are effective in identifying essential nodes in complex networks. Also, the Principal Component Analysis reveals that the Kendall centrality correlation profile can be used to describe the metabolic networks and distinguish them from their random counter-parts with the preserved degree distribution.