Related papers: Posets and spaces of $k$-noncrossing RNA Structure…
The various types of retinal neurons are each positioned at their respective depths within the retina where they are believed to be assembled as orderly mosaics, in which like-type neurons minimize proximity to one another. Two common…
RNA is a vital biomolecule with numerous roles and functions within cells, and interest in targeting it for therapeutic purposes has grown significantly in recent years. However, fully understanding and predicting RNA behavior, particularly…
A Steiner structure $\dS = \dS_q[t,k,n]$ is a set of $k$-dimensional subspaces of $\F_q^n$ such that each $t$-dimensional subspace of $\F_q^n$ is contained in exactly one subspace of $\dS$. Steiner structures are the $q$-analogs of Steiner…
A hierarchical model for the growth of planar arch structures for RNA secondary structures is presented, and shown to be equivalent to a tree-growth model. Both models can be solved analytically, giving access to scaling functions for large…
The notion of regular cell complexes plays a central role in topological combinatorics because of its close relationship with posets. A generalization, called totally normal cellular stratified spaces, was introduced by the third author by…
DNA and RNA are generally regarded as central molecules in molecular biology. Recent advancements in the field of DNA/RNA nanotechnology successfully used DNA/RNA as programmable molecules to construct molecular machines and nanostructures…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
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…
The growing significance of RNA engineering in diverse biological applications has spurred interest in developing AI methods for structure-based RNA design. While diffusion models have excelled in protein design, adapting them for RNA…
Multicellular rosettes are observed in different situations such as morphogenesis, wound healing, and cancer progression. While some molecular insights have been gained to explain the presence of these assemblies of five or more cells…
We describe quantitatively a RNA molecule under the influence of an external force exerted at its two ends as in a typical single-molecule experiment. Our calculation incorporates the interactions between nucleotides by using the…
The conformation space of a 20-residue antiparallel $\beta$-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. The…
A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a…
Developing an idea of Kapranov and Voevodsky, we introduce a model of weak omega-categories based on directed complexes, combinatorial presentations of pasting diagrams. We propose this as a convenient framework for higher-dimensional…
The classic Voronoi cells can be generalized to a higher-order version by considering the cells of points for which a given $k$-element subset of the set of sites consists of the $k$ closest sites. We study the structure of the $k$-order…
Geometric Graph Neural Networks (GNNs) and Transformers have become state-of-the-art for learning from 3D protein structures. However, their reliance on message passing prevents them from capturing the hierarchical interactions that govern…
The Poland-Scheraga model for DNA denaturation, besides playing a central role in applications, has been widely studied in the physical and mathematical literature over the past decades. More recently a natural generalization has been…
Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…