Evolutionary of Online Social Networks Driven by Pareto Wealth Distribution and Bidirectional Preferential Attachment

Understanding of evolutionary mechanism of online social networks is greatly significant for the development of network science. However, present researches on evolutionary mechanism of online social networks are neither deep nor clear enough. In this study, we empirically showed the essential evolution characteristics of Renren online social network. From the perspective of Pareto wealth distribution and bidirectional preferential attachment, the origin of online social network evolution is analyzed and the evolution mechanism of online social networks is explained. Then a novel model is proposed to reproduce the essential evolution characteristics which are consistent with the ones of Renren online social network, and the evolutionary analytical solution to the model is presented. The model can also well predict the ordinary power-law degree distribution. In addition, the universal bowing phenomenon of the degree distribution in many online social networks is explained and predicted by the model. The results suggest that Pareto wealth distribution and bidirectional preferential attachment can play an important role in the evolution process of online social networks and can help us to understand the evolutionary origin of online social networks. The model has significant implications for dynamic simulation researches of social networks, especially in information diffusion through online communities and infection spreading in real societies.Comment: 19 pages, 8 figures,31 reference

Oscillation of solutions of some higher order linear differential equations

In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k)}+B_{k-1}f^{(k-1)}+\cdots+B_1f'+B_0f=F$$ where $B_j(z) (j=0,1,\ldots,k-1)$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li

Bounds for the sums of zeros of solutions of u(m)=P(z)uu^{(m)}=P(z)u where PP is a polynomial

The main purpose of this paper is to consider the differential equation $u^{(m)}=P(z)u$ $(m\geq 2)$ where $P$ is a polynomial with in general complex coefficients. Let $z_{k}(u),$ $k=1,2,\ldots$ be the zeros of a nonzero solution $u$ to that equation. We obtain bounds for the sums $$\sum_{k=1}^{j}\frac{1}{|z_{k}(u)|}\quad (j\in\mathbb{N})$$ which extend some recent results proved by Gil'

Involvement of Fenton chemistry in rice straw degradation by the lignocellulolytic bacterium Pantoea ananatis Sd-1

Additional file 7: Table S2. Primers used for quantitative real time-PCR

Uniqueness and value distribution for q-shifts of meromorphic functions

In this paper, we deal with value distribution for q-shift polynomials of transcendental meromorphic functions with zero order and obtain some results which improve the previous theorems given by Liu and Qi [18]. In addition, we investigate value sharing for q-shift polynomials of transcendental entire functions with zero order and obtain some results which extend the recent theorem given by Liu, Liu and Cao [17]

Benzoxime inhibits matrix metalloproteinase-13 activation and cartilage damage in osteoarthritis rats via inhibition of NF-κB pathway

Purpose: To investigate the effect of benzoxime on degradation of  articular cartilage in a rat model of osteoarthritis (OA), and the mechanism involved.Methods: The OA rat model was prepared by injecting monosodium  iodoacetate (MIA) intra-articularly to Wistar rats. Rats in the treatment group were given benzoxime (5 mg/kg) daily for 21 days through the intra-articular route. The animals were then examined for behavioral changes by assessment of asymmetry in bearing weight and paw  withdrawal threshold of the hind limb. Western blot assay was used for the analysis of inflammatory cytokine expressions.Results: The expression of P2X purinoceptor 7 receptor (P2X7R) mRNA was significantly elevated in the OA rats (p < 0.02). However, benzoxime treatment caused a marked decrease in the level of P2X1-8R mRNA. Benzoxime treatment also prevented asymmetry in bearing weight, decreased paw withdrawal threshold, and inhibited the expressions of interleukin-1β, interleukin-6 and tumor necrosis factor-α in plasma and cartilage. Moreover, benzoxime exhibited significant inhibitory effects on the expressions of P2X7R, matrix metalloproteinase (MMP)-13 and prostaglandin E2 (PGE2) in cartilage tissue. It also significantly  suppressed OA-induced increases in the levels of inhibitor of nuclear factor-κB (NF-κB) kinase (IKK)α, IKKβ, IκBα and NF-κB p65, and blocked OA-induced increases in the expressions of P2X7R, MMP-13 and PGE2.Conclusion: These results demonstrate that benzoxime prevents cartilage degradation in OA rats by targeting NF-κB signaling pathway. Thus, benzoxime possesses clinical and therapeutic potentials for the prevention of cartilage degradation in OA.Keywords: Interleukin-1β, Purinoceptor-7, Benzoxime, Osteoarthritis, Prostaglandin, Matrix metalloproteinase

Antitumor Cyclic Hexapeptides from Rubia Plants: History, Chemistry, and Mechanism (2005–2011)

Rubiaceae-type cyclopeptides (RAs), cyclic hexapeptides from Rubia plants, have shown potential antitumor activity in vitro and in vivo. Based on the review about plant cyclopeptides (Chem. Rev., 2006, 106: 840), this mini-review will highlight new progress on the discovery, synthesis, and mechanism of RAs isolated during 2005 to 2011, covering recent work in our group

Study on the One-Proton Halo Structure in 23^{23}Al

The Glauber theory has been used to investigate the reaction cross section of proton-rich nucleus $^{23}$Al. A core plus a proton structure is assumed for $^{23}$Al. HO-type density distribution is used for the core while the density distribution for the valence proton is calculated by solving the eigenvalue problem of Woods-Saxon potential. The transparency function in an analytical expression is obtained adopting multi-Gaussian expansion for the density distribution. Coulomb correction and finite-range interaction are introduced. This modified Glauber model is apt for halo nuclei. A dominate s-wave is suggested for the last proton in $^{23}$Al from our analysis which is possible in the RMF calculation.Comment: 4 pages, 4 figure