• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.99-103
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• 2003

In this note we find the exact Probability distribution of d$\_$n, i/ the outdegree of the node i, in a random recursive tree with n nodes. For i = i$\_$n/ increasing as a linear function on n, we show that d$\_$n/,i$\_$n/ is asymptotically normal.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.899-910
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• 2019

In this paper, we enumerate the cardinalities for the set of all vertices of outdegree ${\geq}k$ at level ${\geq}{\ell}$ among all rooted ordered d-trees with n edges. Our results unite and generalize several previous works in the literature.

• Asia Marketing Journal
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• v.11 no.2
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• pp.73-96
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• 2009

In this paper, authors focused on the difference between successful and unsuccessful items in terms of the innovation and imitation parameters of Bass diffusion model. Each item was scraped by members directly from the minihompies they visit. Top 50 items in terms of total number of adoption are classified as successful items and the 50 items whose total number of adoption was just below the average are classified as unsuccessful items. In particular, authors are interested in investigating the role of influentials in the diffusion process. Influentials are defined as those people whose network centrality (Indegree, Outdegree, and Betweeness centrality) was larger than the mean centrality in their social network. Figure 1 shows the plots of number of scraping, cumulative scraping, indegree, outdegree and betweenness of the people who scraped the most popular item among 100 items.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.41-56
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• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.257-268
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• 2007

An oriented graph is a digraph with no symmetric pairs of directed arcs and without loops. The score of a vertex $v_i$ in an oriented graph D is $a_{v_i}\;(or\;simply\;a_i)=n-1+d_{v_i}^+-d_{v_i}^-,\;where\; d_{v_i}^+\;and\;d_{v_i}^-$ are the outdegree and indegree, respectively, of $v_i$ and n is the number of vertices in D. In this paper, we give a new proof of Avery's theorem and obtain some stronger inequalities for scores in oriented graphs. We also characterize strongly transitive oriented graphs.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.2
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• pp.335-344
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• 2020

This study compared the structures and changes of help network between pre-service secondary teachers and pre-journalists who participated in the class related to network analysis to seek ways to activate a professional learning community. For this study, we used Exponential Random Graph Models (ERGM) based on ties as being interdependent and not conventional regression models requiring assumptions of independence between observations. The analysis subjects were 43 pre-service secondary teachers and 29 pre-journalists who responded both early and late in the help network survey. The main results were as follows. First, full models with network structural terms were better than simple models with no structural terms. Second, the effect of transitivity was not statistically significant in the pre-service secondary teachers' network. However, it was statistically significant in the pre-journalists' network. Third, there were effects of reciprocity, indegree popularity, and outdegree activity in the early help network of pre-service secondary teachers. On the contrary, there were only the positive effects of reciprocity and the negative effect of outdegree activity in the late network. Finally, this study demonstrated the possibility in educational fields' application of network structural effects and provided limitations and directions for future research.

• Journal of Animal Science and Technology
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• v.60 no.6
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• pp.11.1-11.7
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• 2018

After pubertal, cohort of small antral follicles enters to gonadotrophin-sensitive development, called recruited follicles. This study was aimed to identify candidate genes in follicular cyclic recruitment via analysis of protein-protein interaction (PPI) network. Differentially expressed genes (DEGs) in ovine granulosa cells of small antral follicles between follicular and luteal phases were accumulated among gene/protein symbols of the Ensembl annotation. Following directed graphs, PTPN6 and FYN have the highest indegree and outdegree, respectively. Since, these hubs being up-regulated in ovine granulosa cells of small antral follicles during the follicular phase, it represents an accumulation of blood immune cells in follicular phase in comparison with luteal phase. By contrast, the up-regulated hubs in the luteal phase including CDK1, INSRR and TOP2A which stimulated DNA replication and proliferation of granulosa cells, they known as candidate genes of the cyclic recruitment.

• Journal of the Korea Society of Computer and Information
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• v.4 no.4
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• pp.15-24
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• 1999

In this paper, we propose a new CPLD technology mapping algorithm improving run-time under time constraint. In our technology mapping algorithm, a given logic equation is constructed as the DAG type, then the DAG is reconstructed by replicating the node that outdegree is more than or equal to 2. As a result. it makes delay time and the number of CLBs, run-time to be minimized. Also, after the number of multi-level is defined and cost of each nodes is calculated, the graph is partitioned in order to fit to k that is the number of OR term within CLB. The partitioned nodes are merged through collapsing and bin packing is performed in order to fit to the number of OR term within CLB.

• The Journal of the Korea Contents Association
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• v.17 no.12
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• pp.49-63
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• 2017

Interdisciplinary convergence research is widely seen as a collaborative research between different disciplines, which is often driven by common agenda or problems in pursuit of a particular common objective. Thus, the purpose of interdisciplinary cooperation in convergence research is to bring each discipline's unique perspective together with the academic expertise of researchers in order to share common problems that cannot be solved effectively without research partnership. We present empirical evidence on how interdisciplinary research relationships are formed to facilitate research networking in convergence relations. In particular, we used network analysis to investigate how interdisciplinary linkages and convergence research networks has formed over time. We found that the convergence research networks were implemented by the interdisciplinary convergence research support program as intended. We did find that research field with high indegree and outdegree in a network played critical roles on the dynamics and degree of interdisciplinarity. Finally, we could find evidence that the role of liaison brokers triggered relational dynamics in interdisciplinary research collaboration.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.6
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• pp.9-17
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• 1999

In this paper, we propose a new technology mapping algorithm for CPLD under time constraint. In our technology mapping algorithm, a given logic equation is constructed as the DAG type, then the DAG is reconstructed by replicating the node that outdegree is more than or equal to 2. As a result, it makes delay time and the number of CLBs to be minimized. Also, after the number of multi-level is defined and cost of each nodes is calculated, the graph is partitioned in order to fit to k that is the number of OR term within CLB. The partitioned nodes are merged through collapsing and bin packing is performed in order to fit to the number of OR term within CLB. In the results of experiments to MCNC circuits for logic synthesis benchmark, we can shows that proposed technology mapping algorithm reduces delay time and the number of CLBs much more than the existing tools of technology mapping algoritm.