Related papers: Combinatorial Analysis for Pseudoknot RNA with Com…
Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to…
The idea of this project is to study the protein structure and sequence relationship using the hidden markov model and artificial neural network. In this context we have assumed two hidden markov models. In first model we have taken protein…
RNA secondary structures of increasing complexity are probed combining single molecule stretching experiments and stochastic unfolding/refolding simulations. We find that force-induced unfolding pathways cannot usually be interpretated by…
In this short paper, we explore relationship between various models of complex networks with pinning controllers.
Given a random RNA secondary structure, $S$, we study RNA sequences having fixed ratios of nuclotides that are compatible with $S$. We perform this analysis for RNA secondary structures subject to various base pairing rules and minimum arc-…
Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In…
The probability of a random polygon (or a ring polymer) having a knot type $K$ should depend on the complexity of the knot $K$. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially…
Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of crossings. For each family, we express the generating function…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build…
The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional…
In this paper, we introduce polynomial time algorithms that generate random $k$-noncrossing partitions and 2-regular, $k$-noncrossing partitions with uniform probability. A $k$-noncrossing partition does not contain any $k$ mutually…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes…
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
Understanding the structure and dynamics of biological networks is one of the important challenges in system biology. In addition, increasing amount of experimental data in biological networks necessitate the use of efficient methods to…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…