Scale-free behavior of networks with the copresence of preferential and uniform attachment rules

Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential attachment model, whose modifications are interesting for two main reasons: to analyze more realistic models and to study the robustness of the scale free behavior of the degree distribution. We introduce and study a model which takes into account two different attachment rules: a preferential attachment mechanism (with probability 1-p) that stresses the rich get richer system, and a uniform choice (with probability p) for the most recent nodes. The latter highlights a trend to select one of the last added nodes when no information is available. The recent nodes can be either a given fixed number or a proportion (\alpha n) of the total number of existing nodes. In the first case, we prove that this model exhibits an asymptotically power-law degree distribution. The same result is then illustrated through simulations in the second case. When the window of recent nodes has constant size, we herein prove that the presence of the uniform rule delays the starting time from which the asymptotic regime starts to hold. The mean number of nodes of degree k and the asymptotic degree distribution are also determined analytically. Finally, a sensitivity analysis on the parameters of the model is performed

Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

The problem of counting plane trees with $n$ edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schr\"oder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions was independently studied by Klazar. We present three parity reversing involutions, one for unlabelled plane trees, the other for labelled plane trees and one for 2-Motzkin paths which are in one-to-one correspondence with Dyck paths.Comment: 8 pages, 4 figure

Servant Leadership Relationship to Emotional Demands, Stress, and Well-Being of the Leader

Previous studies have investigated the outcomes of servant leadership on the followers and organization. The present study investigated the outcomes of practicing servant leadership on the leader by identifying the relationships between servant leadership and emotional demand, stress, and well-being. Eighty-seven leaders completed a survey on their leadership behaviors, emotional labor, emotional intelligence, stress, and well-being. Two servant leadership scores were used to analyze the relationships. Multiple correlation analyses, linear regressions, and hierarchical multiple regressions were conducted and found partial support across all hypotheses. Overall trending patterns indicated servant leadership had a positive correlation with emotional labor, emotional intelligence, and stress, and a negative correlation with well-being. Results also indicated that emotional labor mediated the relationship between servant leadership and emotional intelligence, and between servant leadership and well-being. Servant leadership is beneficial to the organization, but can be negative to the leader’s health if suggested considerations are not incorporated

Framing a Dual-Task and its Effects on Performance and Mood

The present study investigated the framing of a dual-task and its effects on performance and mood. Framing a dual-task as either multitasking or an interruption deals with the interpretation of working on two or more tasks simultaneously, such as the nature of the presentation of the secondary task. A total of 81 undergraduate students (59 female) were recruited from Arcadia University to participate in the experiment. Participants were randomly assigned to either be multitasking (n = 28), interrupted (n = 28), or single-tasking (n = 25) with an essay task and an audio task. Participants’ moods were surveyed before and after the tasks, and their perceived performance and actual performance on both tasks were calculated. A one-way analysis of variance (ANOVA) showed that tasks framed as multitasking performed the worst, rated lower on their perceived performance, and had a more negative affect than when tasks were framed as an interruption or those single-tasking. Results also found that tasks framed as an interruption rated highest on perceived performance, performed the best, and had a more positive affect than the multitasking and single-tasking conditions. Implications are that actual performance suffers regardless if a dual-task is framed as multitasking or handling an interruption, but will have a slightly better outcome when it is a quick interruption. However, it is best to focus on one task at a time to be more productive and produce minimal errors than to focus on multiple tasks simultaneously