Percolation properties of growing networks under an Achlioptas process

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with the probability $\delta$, a link is formed between two nodes chosen by an AP. We find that there occurs the percolation transition with varying $\delta$ and the critical point $\delta_c=0.5149(1)$ is determined from the power-law behavior of order parameter and the crossing of the fourth-order cumulant at the critical point, also confirmed by the movement of the peak positions of the second largest cluster size to the $\delta_c$. Using the finite-size scaling analysis, we get $\beta/\bar{\nu}=0.20(1)$ and $1/\bar{\nu}=0.40(1)$, which implies $\beta \approx 1/2$ and $\bar{\nu} \approx 5/2$. The Fisher exponent $\tau = 2.24(1)$ for the cluster size distribution is obtained and shown to satisfy the hyperscaling relation.Comment: 4 pages, 5 figures, 1 table, journal submitte

Generalized gravity model for human migration

The gravity model (GM) analogous to Newton's law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but powerful approach relies only on the 'mass' factor represented by the scale of the regions and the 'geometrical' factor represented by the geographical distance. However, when the population has a subpopulation structure distinguished by different attributes, the estimation of the flow solely from the coarse-grained geographical factors in the GM causes the loss of differential geographical information for each attribute. To exploit the full information contained in the geographical information of subpopulation structure, we generalize the GM for population flow by explicitly harnessing the subpopulation properties characterized by both attributes and geography. As a concrete example, we examine the marriage patterns between the bride and the groom clans of Korea in the past. By exploiting more refined geographical and clan information, our generalized GM properly describes the real data, a part of which could not be explained by the conventional GM. Therefore, we would like to emphasize the necessity of using our generalized version of the GM, when the information on such nongeographical subpopulation structures is available.Comment: 14 pages, 6 figures, 2 table

Anti-amyloidogenic effect of menaquinone-7 on betaamyloid production and aggregation

Purpose: To investigate the beneficial effects of menaquinone-7 (MK-7), an isoform of vitamin K2, against beta-amyloid (Aβ) production and aggregation in Alzheimer's disease using in vitro assays. Methods: The cytotoxicity of MK-7 was determined by MTT assay. The amount of Aβ produced and secreted into the supernatant by APP-CHO cells treated with MK-7 was evaluated by ELISA. The expression of β-secretases and ADAM10, a representative α-secretase, was determined using western blot analysis. The production of sAPPβ and sAPPα fragments generated by β-secretases and αsecretase, respectively, were also determined by western blot analysis. The effect on Aβ aggregation was assessed using Thioflavin T (Th T) assay. Results: MK-7 (up to 75 nM) significantly decreased Aβ production in APP-CHO cells. This was accompanied by decreased expression of β-secretase and lower production of sAPPβ (p < 0.05). However, expression of ADAM10 and production of sAPPα were not significantly affected. In contrast, MK-7 significantly decreased Aβ aggregation in a dose-dependent manner (p < 0.05). Conclusion: MK-7 exerts anti-amyloidogenic effects via decreased production and lower aggregation of Aβ into oligomers and fibrils. Therefore, dietary supplementation with MK-7 may be beneficial for the prevention of Alzheimer’s disease