Related papers: Canonical RNA pseudoknot structures
In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m > 1. We use Koszul cohomology with it to prove…
The family of snarks -- connected bridgeless cubic graphs that cannot be 3-edge-coloured -- is well-known as a potential source of counterexamples to several important and long-standing conjectures in graph theory. These include the cycle…
Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant,…
(Abridged) Designing computationally efficient algorithms in the agnostic learning model (Haussler, 1992; Kearns et al., 1994) is notoriously difficult. In this work, we consider agnostic learning with membership queries for touchstone…
A linear chord diagram canonically determines a fatgraph and hence has an associated genus $g$. We compute the natural generating function ${\bf C}_g(z)=\sum_{n\geq 0} {\bf c}_g(n)z^n$ for the number ${\bf c}_g(n)$ of linear chord diagrams…
Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…
We further develop the large $ N $ formalism presented by some of us in earlier works in order to recursively calculate the partition function of a singly pseudoknotted RNA. We demonstrate that this calculation takes time proportional to…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
We consider a certain abstract of RNA secondary structures, which is closely related to RNA shapes. The generating function counting the number of the abstract structures is obtained by means of Narayana numbers and 2-Motzkin paths, through…
The primary structure of a ribonucleic acid (RNA) molecule can be represented as a sequence of nucleotides (bases) over the alphabet {A, C, G, U}. The secondary or tertiary structure of an RNA is a set of base pairs which form bonds between…
Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations…
A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous…
We construct canonical absolute parallelisms over real-analytic manifolds equipped with $2$-nondegenerate, hypersurface-type CR structures of arbitrary odd dimension not less than $7$ whose Levi kernel has constant rank belonging to a broad…
In Part I of this series we described three algorithms that construct canonical tree-decompositions of graphs which distinguish all their k-blocks and tangles of order k. We now establish bounds on the number of parts in these…
An elementary, at the undergraduate level derivation is given of precise upper bounds of the number of various RNA secondary structures. The method works when the generating function has multiple singularities at the circle of convergence,…
Networks of silicon nanowires possess intriguing electronic properties surpassing the predictions based on quantum confinement of individual nanowires. Employing large-scale atomistic pseudopotential computations, as yet unexplored branched…
We propose a two-level stochastic context-free grammar (SCFG) architecture for parametrized stochastic modeling of a family of RNA sequences, including their secondary structure. A stochastic model of this type can be used for maximum a…
A canonical Huffman sequence is characterized by a zero inner-product between itself and each of its shifted copies, except at their largest relative shifts: their aperiodic auto-correlation then becomes delta-like, a single central peak…
Knots have been considered to be useful models for simulating molecular chains such as DNA and proteins. One quantity that we are interested on molecular knots is the minimum number of monomers necessary to realize a knot. In this paper we…