Related papers: Time and Space Efficient Algorithms for RNA Foldin…
The secondary structure that maximizes the number of non-crossing matchings between complimentary bases of an RNA sequence of length n can be computed in O(n^3) time using Nussinov's dynamic programming algorithm. The Four-Russians method…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
Motivation: Predicting the secondary structure of an RNA sequence is useful in many applications. Existing algorithms (based on dynamic programming) suffer from a major limitation: their runtimes scale cubically with the RNA length, and…
Ab initio RNA secondary structure predictions have long dismissed helices interior to loops, so-called pseudoknots, despite their structural importance. Here, we report that many pseudoknots can be predicted through long time scales RNA…
It has been shown that minimum free energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble based quantities such…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can…
We formulate the RNA folding problem as an $N\times N$ matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
Many computerized methods for RNA-RNA interaction structure prediction have been developed. Recently, $O(N^6)$ time and $O(N^4)$ space dynamic programming algorithms have become available that compute the partition function of RNA-RNA…
The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…
RNAs self-interact through hydrogen-bond base-pairing between nucleotides and fold into specific, stable structures that substantially govern their biochemical behaviour. Experimental characterization of these structures remains difficult,…
The Dyck language, which consists of well-balanced sequences of parentheses, is one of the most fundamental context-free languages. The Dyck edit distance quantifies the number of edits (character insertions, deletions, and substitutions)…
A noticeable fraction of Algorithms papers in the last few decades improve the running time of well-known algorithms for fundamental problems by logarithmic factors. For example, the $O(n^2)$ dynamic programming solution to the Longest…
The information-encoding molecules RNA and DNA form a combinatorially large set of secondary structures through nucleic acid base pairing. Thermodynamic prediction algorithms predict favoured, or minimum free energy (MFE), secondary…
RNA secondary structure prediction is widely used to understand RNA function. Recently, there has been a shift away from the classical minimum free energy (MFE) methods to partition function-based methods that account for folding ensembles…
The classical Sankoff algorithm for the simultaneous folding and alignment of homologous RNA sequences is highly influential, but it suffers from two major limitations in efficiency and modeling power. First, it takes $O(n^6)$ for two…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
RNA co-transcriptionality, where RNA is spliced or folded during transcription from DNA templates, offers promising potential for molecular programming. It enables programmable folding of nano-scale RNA structures and has recently been…
The structure of an RNA molecule plays a significant role in its biological function. Predicting structure given a one dimensional sequence of RNA nucleotide bases is a difficult and important problem. Many computer programs (known as in…
Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…