There is a large, popular, and growing literature on "scale-free" networks with the Internet along with metabolic networks representing perhaps the canonical examples. While this has in many ways reinvigorated graph theory, there is unfortunately no consistent, precise definition of scale-free graphs and few rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and that the most celebrated claims regarding the Internet and biology are verifiably false. In this paper, we introduce a structural metric that allows us to differentiate between all simple, connected graphs having an identical degree sequence, which is of particular interest when that sequence satisfies a power law relationship. We demonstrate that the proposed structural metric yields considerable insight into the claimed properties of SF graphs and provides one possible measure of the extent to which a graph is scale-free. This structural view can be related to previously studied graph properties such as the various notions of self-similarity, likelihood, betweenness and assortativity. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the current literature, and offers a rigorous and quantitative alternative, while suggesting the potential for a rich and interesting theory. This paper is aimed at readers familiar with the basics of Internet technology and comfortable with a theorem-proof style of exposition, but who may be unfamiliar with the existing literature on scale-free networks.

Single-layer single-crystalline SnSe nanosheet with four-atomic thickness of ~1.0 nm and lateral size of ~300 nm is presented here by using a one-pot synthetic method. It is found that 1,10-phenanthroline plays an important role in determining the morphology of the SnSe product as three-dimensional SnSe nanoflowers are obtained in the absence of 1,10-phenanthroline while keeping other reaction parameters the same. The evolution process study discloses that single-crystalline nanosheets are obtained from the coalescence of the SnSe nucleus in an orientated attachment mechanism. Band gap determination and optoelectronic test based on hybrid films of SnSe and poly(3-hexylthiophene) indicate the great potential of the ultrathin SnSe nanosheets in photodector and photovoltaic, and so forth.

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A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved designs for resource provisioning. Previous studies of topology have focused on interpreting measurements or on phenomenological descriptions and evaluation of graph-theoretic properties of topology generators. We propose a complementary approach of combining a more subtle use of statistics and graph theory with a first-principles theory of router-level topology that reflects practical constraints and tradeoffs. While there is an inevitable tradeoff between model complexity and fidelity, a challenge is to distill from the seemingly endless list of potentially relevant technological and economic issues the features that are most essential to a solid understanding of the intrinsic fundamentals of network topology. We claim that very simple models that incorporate hard technological constraints on router and link bandwidth and connectivity, together with abstract models of user demand and network performance, can successfully address this challenge and further resolve much of the confusion and controversy that has surrounded topology generation and evaluation.

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Abstract-Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet.Index Terms-Degree-based generators, heuristically optimal topology, network design, network topology, router configuration, topology metrics.

BackgroundThe majority of breast cancer patients die of metastasis rather than primary tumors, whereas the molecular mechanisms orchestrating cancer metastasis remains poorly understood. Long noncoding RNAs (lncRNA) have been shown to regulate cancer occurrence and progression. However, the lncRNAs that drive metastasis in cancer patients and their underlying mechanisms are still largely unknown.MethodslncRNAs highly expressed in metastatic lymph nodes were identified by microarray. Survival analysis were made by Kaplan-Meier method. Cell proliferation, migration, and invasion assay was performed to confirm the phenotype of LINC02273. Tail vein model and mammary fat pad model were used for in vivo study. RNA pull-down and RIP assay were used to confirm the interaction of hnRNPL and LINC02273. Chromatin isolation by RNA purification followed by sequencing (ChIRP-seq), RNA-seq, ChIP-seq, and luciferase reporter assay reveal hnRNPL-LINC02273 regulates AGR2. Antisense oligonucleotides were used for in vivo treatment.ResultsWe identified a novel long noncoding RNA LINC02273, whose expression was significantly elevated in metastatic lesions compared to the primary tumors, by genetic screen of matched tumor samples. Increased LINC02273 promoted breast cancer metastasis in vitro and in vivo. We further showed that LINC02273 was stabilized by hnRNPL, a protein increased in metastatic lesions, in breast cancer cells. Mechanistically, hnRNPL-LINC02273 formed a complex which activated AGR2 transcription and promoted cancer metastasis. The recruitment of hnRNPL-LINC02273 complex to AGR2 promoter region epigenetically upregulated AGR2 by augmenting local H3K4me3 and H3K27ac levels. Combination of AGR2 and LINC02273 was an independent prognostic factor for predicting breast cancer patient survival. Moreover, our data revealed that LINC02273-targeting antisense oligonucleotides (ASO) substantially inhibited breast cancer metastasis in vivo.ConclusionsOur findings uncover a key role of LINC02273-hnRNPL-AGR2 axis in breast cancer metastasis and provide potential novel therapeutic targets for metastatic breast cancer intervention.