Related papers: Endhered patterns in matchings and RNA
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,…
Signed networks are frequently observed in real life with additional sign information associated with each edge, yet such information has been largely ignored in existing network models. This paper develops a unified embedding model for…
We define a class of properties on random plane trees, which we call subtree additive properties, inspired by the combinatorics of certain biologically-interesting properties in a plane tree model of RNA secondary structure. The class of…
We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the…
Solving the RNA inverse folding problem is a critical prerequisite to RNA design, an emerging field in bioengineering with a broad range of applications from reaction catalysis to cancer therapy. Although significant progress has been made…
An essential quantity to ensure evolvability of populations is the navigability of the genotype space. Navigability relies on the existence of sufficiently large genotype networks, that is ensembles of sequences with the same phenotype that…
We present some results on the proportion of permutations of length $n$ containing certain mesh patterns as $n$ grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and…
Large-scale coarse-grained molecular dynamics simulations of inhomogeneous gel networks were performed to investigate abnormal butterfly patterns in two-dimensional scattering. The networks were diamond lattice-based with distributions in…
The probability distributions for bending angles in double helical DNA obtained in all-atom molecular dynamics simulations are compared with theoretical predictions. The computed distributions remarkably agree with the worm-like chain…
The knots-quivers correspondence states that various characteristics of a knot are encoded in the corresponding quiver and the moduli space of its representations. However, this correspondence is not a bijection: more than one quiver may be…
The combinatorics of RNA plays a central role in biology. Mathematical biologists have several commonly-used models for RNA: words in a fixed alphabet (representing the primary sequence of nucleotides) and plane trees (representing the…
This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each…
Given the importance of non-coding RNAs to cellular regulatory functions and rapid growth of RNA transcripts, computational prediction of RNA tertiary structure remains highly demanded yet significantly challenging. Even for a short RNA…
We explore numerically, analytically, and experimentally the relationship between quasi-normal modes (QNMs) and transmission resonance (TR) peaks in the transmission spectrum of one-dimensional (1D) and quasi-1D open disordered systems. It…
We show the expected order of RNA saturated secondary structures of size $n$ is $\log_4n(1+O(\frac{\log_2n}{n}))$, if we select the saturated secondary structure uniformly at random. Furthermore, the order of saturated secondary structures…
Formation of a pseudoknot in the conserved RNA core domain in the ribonucleoprotein human telomerase is required for function. In vitro experiments show that the pseudoknot (PK) is in equilibrium with an extended hairpin (HP) structure. We…
Mining tasks over sequential data, such as clickstreams and gene sequences, require a careful design of embeddings usable by learning algorithms. Recent research in feature learning has been extended to sequential data, where each instance…