Related papers: A growth model for RNA secondary structures
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small…
Despite great interest in solving RNA secondary structures due to their impact on function, it remains an open problem to determine structure from sequence. Among experimental approaches, a promising candidate is the "chemical modification…
An RNA secondary structure is designable if there is an RNA sequence which can attain its maximum number of base pairs only by adopting that structure. The combinatorial RNA design problem, introduced by Hale\v{s} et al. in 2016, is to…
We study a model of growing planar tree graphs where in each time step we separate the tree into two components by splitting a vertex and then connect the two pieces by inserting a new link between the daughter vertices. This model…
A simple growth model for DNA evolution is introduced which is analytically solvable and reproduces the observed statistical behavior of real sequences.
HiRE-RNA is a simplified, coarse-grained RNA model for the prediction of equilibrium configurations, dynamics and thermodynamics. Using a reduced set of particles and detailed interactions accounting for base-pairing and stacking we show…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics and…
Computational systems and methods are often being used in biological research, including the understanding of cancer and the development of treatments. Simulations of tumor growth and its response to different drugs are of particular…
We present a simple kinetic model for the assembly of small single-stranded RNA viruses that can be used to carry out analytical packaging contests between different types of RNA molecules. The RNA selection mechanism is purely kinetic and…
We propose a dynamical model for the secondary structure of DNA, which is based on the finite stacking enthalpies used in thermodynamics calculations. In this model, the two strands can separate and the bases are allowed to rotate…
We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched…
Vital to primary visual processing, retinal circuitry shows many similar structures across a very broad array of species, both vertebrate and non-vertebrate, especially functional components such as lateral inhibition. This surprisingly…
Motivation: Single cell RNA sequencing (scRNA-seq) data makes studying the development of cells possible at unparalleled resolution. Given that many cellular differentiation processes are hierarchical, their scRNA-seq data is expected to be…
We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to…
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,…
RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix…
In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical…