Related papers: Expected degree for RNA secondary structure networ…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the node's neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks,…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
RNA structure prediction is a challenging problem, especially with pseudoknots. Recently, there has been a shift from the classical minimum free energy-based methods (MFE) to partition function-based ones that assemble structures using…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes…
A useful property of a network that can be used to characterize many systems is the degree distribution. However, many complex networks exhibit higher--order degree correlations that must be studied through other means, such as clustering…
Precisely quantifying the heterogeneity or disorder of a network system is very important and desired in studies of behavior and function of the network system. Although many degree-based entropies have been proposed to measure the…
In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is…
We have established an RNA Mapping Database (RMDB) to enable a new generation of structural, thermodynamic, and kinetic studies from quantitative single-nucleotide-resolution RNA structure mapping (freely available at…
In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…
The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base…
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each…
We prove that, for every set of $n$ points $\mathcal{P}$ in $\mathbb{R}^2$, a random plane graph drawn on $\mathcal{P}$ is expected to contain less than $n/10.18$ isolated vertices. In the other direction, we construct a point set where the…
In this paper, we propose an end-to-end deep learning model, called E2Efold, for RNA secondary structure prediction which can effectively take into account the inherent constraints in the problem. The key idea of E2Efold is to directly…
Arc-annotated sequences are useful for representing structural information of RNAs and have been extensively used for comparing RNA structures in both terms of sequence and structural similarities. Among the many paradigms referring to…
(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…