Related papers: Zigzag Stacks and m-Regular Linear Stacks
The high-throughput short-reads RNA-seq protocols often produce paired-end reads, with the middle portion of the fragments being unsequenced. We explore if the full-length fragments can be computationally reconstructed from the sequenced…
The Human Genome Project has led to an exponential increase in data related to the sequence, structure, and function of biomolecules. Bioinformatics is an interdisciplinary research field that primarily uses computational methods to analyze…
A new formalism for calculation of the partition function of single stranded nucleic acids is presented. Secondary structures and the topology of structure elements are the level of resolution that is used. The folding model deals with…
The assembly of banana-shaped rodlike proteins on membranes, and the associated membrane shape transformations, are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
Given usefulness of protein language models (LMs) in structure and functional inference, RNA LMs have received increased attentions in the last few years. However, these RNA models are often not compared against the same standard. Here, we…
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,…
Jaeger's directed cycle double cover conjecture can be formulated as a problem of existence of special perfect matchings in a class of graphs that we call hexagon graphs. In this work, we explore the structure of hexagon graphs. We show…
Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…
Monte Carlo simulations of a Miyazawa-Jernigan lattice-polymer model indicate that, depending on the native's structure geometry, the model exhibits two broad classes of folding mechanisms for two-state folders. Folding to native structures…
Structural prediction has long been considered critical in RNA research, especially following the success of AlphaFold2 in protein studies, which has drawn significant attention to the field. While recent advances in machine learning and…
First, we consider order-$n$ ribbon tilings of an $M$-by-$N$ rectangle $R_{M,N}$ where $M$ and $N$ are much larger than $n$. We prove the existence of the growth rate $\gamma_n$ of the number of tilings and show that $\gamma_n \leq (n-1)…
We review Migdal's Theory of Finite Fermi Systems and its application to the structure of nuclei. The theory is an extension of Landau's Theory of Interacting Fermi Systems. In the first part the basic formulas are derived within the many…
Recent advancements in machine learning techniques for protein folding motivate better results in its inverse problem -- protein design. In this work we introduce a new graph mimetic neural network, MimNet, and show that it is possible to…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
RNA secondary structure is an important computational model to understand how genetic variation maps into phenotypic (structural) variation. Evolutionary innovation in RNA structures is facilitated by neutral networks, large connected sets…
Prediction of one-dimensional protein structures such as secondary structures and contact numbers is useful for the three-dimensional structure prediction and important for the understanding of sequence-structure relationship. Here we…
An extended formulation of a polyhedron $P$ is a linear description of a polyhedron $Q$ together with a linear map $\pi$ such that $\pi(Q)=P$. These objects are of fundamental importance in polyhedral combinatorics and optimization theory,…
Prediction of protein secondary structure from the amino acid sequence is a classical bioinformatics problem. Common methods use feed forward neural networks or SVMs combined with a sliding window, as these models does not naturally handle…