Mathematical modeling of nonlinear dynamic system of the truck crane

Ivanov, Sergei Evgenievich

doi:10.12988/ces.2016.6218

Cited by 4 publications

(3 citation statements)

References 13 publications

(11 reference statements)

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“…For social network, centrality by degree determines the importance of the participant, depending on the number of friends or the connections in the graph. The centrality by degree for vertices in order on figure 1 is equal to: Cd={12, 13,9,12,9,18,24,22,12,20,25,20,13,16,23,18,24,18,18,22,15,25,24,19,22,19,22,17,11,19,21,31,26,16,31,19,30,15,24,22,32,28,30,20,15,22,16,25,22,28,31,17,22,23,17,9,13,18,…”

Section: The Methods For Clustering Graph Models Based On the Analysimentioning

confidence: 99%

“…Defining communities in social networks necessary for their classification, grouping of participants, hypothesis testing. The analysis of models can be produced by various methods of mathematical modeling [12][13][14][15]. The basic methods of research communities in social networks are clustering methods in graph models: Modularity, Centrality, Hierarchical, Spectral, K-means, PAM [16].…”

Section: Introductionmentioning

confidence: 99%

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The clustering methods in graph models of social networks

Zudilova¹,

Ivanov²

2017

ams

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Analysis of social networks based on graph models allows determining the associated subgroups and visualizing the results. The basic methods of research communities in graph models of social networks are clustering methods: Modularity, Centrality, Hierarchical, Spectral, K-means, PAM (Partitioning Around Medoids). In the methods of searching for communities, the results essentially depend on the chosen metric-the measure of similarity of the participants. As a measure of similarity, we proposed to choose an averaged centrality, which takes into account a number of properties for participants. The new method for clustering graph models based on averaging of centrality is represented. As an example, clustering of a subgroup of a social network consisting of hundreds of participants is performed. The results of clustering for the proposed method are compared with the main methods. The similarities of the distinguished subgroups are verified by means of the cosine and correlation coefficients of vertex similarity, the Jaccard and Dice similarity coefficients. We proposed a new metric-the average coefficient based on the coefficients of vertex similarity. A comparative analysis of clustering results showed that the proposed method for clustering graph models has an accuracy in determining clusters that is comparable with methods-Spectral, Hierarchical, K-Means, and surpasses the accuracy of methods-PAM, Centrality, Modularity

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Section: The Methods For Clustering Graph Models Based On the Analysimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The clustering methods in graph models of social networks

Zudilova¹,

Ivanov²

2017

ams

Self Cite

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“…In this case these conditions help to solve problems of control and stabilization. A delay effect on the stability of the equilibrium point was studied in [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

Stability in the process with lag of interaction between mining and processing industries

Kirjanen,

Malafeyev,

Redinskikh

2017

Preprint

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A mathematical model of dynamic interaction between mining and processing industries is formalized and studied in the paper. The process of interaction is described by a system of two delay differential equations. The criterion for asymptotic stability of nontrivial equilibrium point is obtained when both industries co-work steadily. The problem is reduced to finding stability criterion for quasi-polynomial of second order. Time intervals between deliveries of raw materials which make it possible to preserve stable interaction between the two industries are found.

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