Some asymptotic properties of duplication graphs

Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are studied: pure duplication growth, and two two-parameter models in which duplication forms one element of the growth dynamics. A power-law degree distribution is found to emerge in all three models. However, the parameter space of the latter two models is characterized by a range of parameter values for which duplication is the predominant mechanism of graph growth. For parameter values that lie in this ``duplication-dominated'' regime, it is shown that the degree distribution either approaches zero asymptotically, or approaches a non-zero power-law degree distribution very slowly. In either case, the approach to the true asymptotic degree distribution is characterized by a dependence of the scaling exponent on properties of the initial degree distribution. It is therefore conjectured that duplication-dominated, scale-free networks may contain identifiable remnants of their early structure. This feature is inherited from the idealized model of pure duplication growth, for which the exact finite-size degree distribution is found and its asymptotic properties studied.Comment: 19 pages, including 3 figure

Probability distribution of persistent spins in a Ising chain

We study the probability distribution $Q(n,t)$ of $n(t)$, the fraction of spins unflipped till time $t$, in a Ising chain with ferromagnetic interactions. The distribution shows a peak at $n=n_{max}$ and in general is non-Gaussian and asymmetric in nature. However for $n>n_{max}$ it shows a Gaussian decay. A data collapse can be obtained when $Q(n,t)/L^{\alpha}$ versus $(n-n_{max})L^{\beta}$ is plotted with $\alpha \sim 0.45$ and $\beta \sim 0.6$. Interestingly, $n_{max}(t)$ shows a different behaviour compared to $= P(t)$, the persistence probability which follows the well-known behaviour $P(t)\sim t^{-\theta}$. A quantitative estimate of the asymmetry and non-Gaussian nature of $Q(n,t)$ is made by calculating its skewness and kurtosis.Comment: 4 pages, submitted to J. Phys

Phase ordering on small-world networks with nearest-neighbor edges

We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined and compared with the global coherence in the corresponding \xy model without quenched randomness. It is found that in the appropriate regime phase ordering emerges at finite temperatures, even for a tiny fraction of shortcuts. Nature of the phase transition is also discussed.Comment: 5 pages, 4 figures, Phys. Rev. E (in press

Self Organized Scale-Free Networks from Merging and Regeneration

We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a network may be viewed as an optimization of efficiency by minimizing redundancy. It is also a mechanism to shorten the distance and thus decrease signaling times between vertices in a complex network. Thus the merging process will in particular be relevant for networks where these issues related to global signaling are of concern

Positron emission tomographic imaging of Copper 64- and Gallium 68-labeled chelator conjugates of the somatostatin agonist Tyr3-octreotate

The bifunctional chelator and radiometal have been shown to have a direct effect on the pharmacokinetics of somatostatin receptor (SSTR)-targeted imaging agents. We evaluated three Y3-TATE analogues conjugated to NOTA-based chelators for radiolabeling with 64 Cu and 68 Ga for small-animal positron emission tomographic/computed tomograhic (PET/CT) imaging. Two commercially available NOTA analogues, p-SCN-Bn-NOTA and NODAGA, were evaluated. The p-SCN-Bn-NOTA analogues were conjugated to Y3- TATE through β-Ala and PEG 8 linkages. The NODAGA chelator was directly conjugated to Y3-TATE. The analogues labeled with 64 Cu or 68 Ga were analyzed in vitro for binding affinity and internalization and in vivo by PET/CT imaging, biodistribution, and Cerenkov imaging ( 68 Ga analogues). We evaluated the effects of the radiometals, chelators, and linkers on the performance of the SSTR subtype 2–targeted imaging agents and also compared them to a previously reported agent, 64 Cu-CB-TE2A-Y3-TATE. We found that the method of conjugation, particularly the length of the linkage between the chelator and the peptide, significantly impacted tumor and nontarget tissue uptake and clearance. Among the 64 Cu- and 68 Ga-labeled NOTA analogues, NODAGA-Y3-TATE had the most optimal in vivo behavior and was comparable to 64 Cu-CB-TE2A-Y3-TATE. An advantage of NODAGA-Y3-TATE is that it allows labeling with 64 Cu and 68 Ga, providing a versatile PET probe for imaging SSTr subtype 2-positive tumors

Evolution of community structure in the world trade web

In this note we study the bilateral merchandise trade flows between 186 countries over the 1948-2005 period using data from the International Monetary Fund. We use Pajek to identify network structure and behavior across thresholds and over time. In particular, we focus on the evolution of trade "islands" in the a world trade network in which countries are linked with directed edges weighted according to fraction of total dollars sent from one country to another. We find mixed evidence for globalization.Comment: To be submitted to APFA 6 Proceedings, 8 pages, 3 Figure

Evolution of reference networks with aging

We study the growth of a reference network with aging of sites defined in the following way. Each new site of the network is connected to some old site with probability proportional (i) to the connectivity of the old site as in the Barab\'{a}si-Albert's model and (ii) to $\tau^{-\alpha}$, where $\tau$ is the age of the old site. We consider $\alpha$ of any sign although reasonable values are $0 \leq \alpha \leq \infty$. We find both from simulation and analytically that the network shows scaling behavior only in the region $\alpha < 1$. When $\alpha$ increases from $-\infty$ to 0, the exponent $\gamma$ of the distribution of connectivities ($P(k) \propto k^{-\gamma}$ for large $k$) grows from 2 to the value for the network without aging, i.e. to 3 for the Barab\'{a}si-Albert's model. The following increase of $\alpha$ to 1 makes $\gamma$ to grow to $\infty$. For $\alpha>1$ the distribution $P(k)$ is exponentional, and the network has a chain structure.Comment: 4 pages revtex (twocolumn, psfig), 5 figure

The posterior use of BMP-2 in cervical deformity surgery does not result in increased early complications: A prospective multicenter study

Study designProspective cohort study.ObjectivesTo describe the rate of short-term complications following the posterior use of recombinant human bone morphogenetic protein-2 (rhBMP-2) in cervical deformity (CD) surgery.MethodsCD patients from 2013 to 2015 were enrolled in a prospective, multicenter database. Patients were divided into those receiving rhBMP-2 (BMP) and no rhBMP-2 (NOBMP). The relationship between BMP use, demographic variables surgical variables, radiographic parameters and complications was evaluated.ResultsA total of 100 patients (47 BMP, 53 NOBMP) were included. Follow-up time averaged 7.6 months (range 3-12 months). An average of 13.6mg of BMP was used per person with 1.49 mg per level. Compared with the NOBMP group, patients in the BMP group were older (P = .03). BMP was more commonly used in patients that and had longer prior fusions (6.0 vs 2.5, P &lt; .01). There were no differences between groups with regards to a history of surgery, Charlson Comorbidity Index, estimated blood loss, operation time, fusion levels, and surgical approach. The maintenance of radiographic parameters at 6-month follow-up was similar. There were no differences in terms of total complication incidence, total complications per person, major complications per person or any specific complication. Linear regression and Pearson correlation analysis did not reveal any strong r2 values (r2 = 0.09, 0.08, 0.06) between the use of BMP and complications (major or operative).ConclusionsBMP use was not directly associated with an increased incidence of early complications in this prospective cohort of operative adult CD patients. Its use was associated with increased number of levels instrumented and fused