Small RNAs (sRNAs) are essential regulatory molecules, and there are three major sRNA classes in plants: microRNAs (miRNAs), phased small interfering RNAs (phased siRNAs or phasiRNAs), and heterochromatic siRNAs (hc-siRNAs). Excluding miRNAs, the other two classes are not well annotated or available in public databases for most sequenced plant genomes. We performed a comprehensive sRNA annotation of 143 plant species that have fully sequenced genomes and next-generation sequencing sRNA data publicly available. The results are available via an online repository called sRNAanno (www.plantsRNAs.org). Compared with other public plant sRNA databases, we obtained was much more miRNA annotations, which are more complete and reliable because of the consistent and highly stringent criteria used in our miRNA annotations. sRNAanno also provides free access to genomic information for >22,721 PHAS loci and >22 million hc-siRNA loci annotated from these 143 plant species. Both miRNA and PHAS loci can be easily browsed to view their main features, and a collection of archetypal trans-acting siRNA 3 (TAS3) genes were annotated separately for quick access. To facilitate the ease of sRNA annotation, sRNAanno provides free service for sRNA annotations to the community. In summary, the sRNAanno database is a great resource to facilitate genomic and genetic research on plant small RNAs.
We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume longrange connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r) ∼ r −δ . Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2 < δ < 4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ < 2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ > 4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ < 1, the percolation transition is mean field. For 1 < δ < 2, the critical exponents depend on δ, while for δ > 2 there is no percolation transition as in regular linear chains.
Abstract. Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we present further support for this claim, based on extensive numerical simulations for model networks embedded on lattices of dimensions d e = 1 and d e = 2. We evaluate the dimension d from the power law scaling of (a) the mass of the network with the Euclidean radius r and (b) the probability of return to the origin with the distance r travelled by the random walker. Both approaches yield the same dimension. For networks with δ < d e , d is infinity, while for δ > 2d e , d obtains the value of the embedding dimension d e . In the intermediate regime of interest d e ≤ δ < 2d e , our numerical results suggest that d decreases continously from−1 for δ close to d e . Finally, we discuss the scaling of the mass M and the Euclidean distance r with the topological distance ℓ (minimum number of links between two sites in the network). Our results suggest that in the intermediate regime d e ≤ δ < 2d e , M (ℓ) and r(ℓ) do not increase with ℓ as a power law but with a stretched exponential,
We study the distribution P(sigma) of the equivalent conductance sigma for Erdös-Rényi (ER) and scale-free (SF) weighted resistor networks with N nodes. Each link has conductance g triple bond e-ax, where x is a random number taken from a uniform distribution between 0 and 1 and the parameter a represents the strength of the disorder. We provide an iterative fast algorithm to obtain P(sigma) and compare it with the traditional algorithm of solving Kirchhoff equations. We find, both analytically and numerically, that P(sigma) for ER networks exhibits two regimes: (i) A low conductance regime for sigma
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