Related papers: Self-Assembling DNA Complexes with a Wheel Graph S…

The macromolecules that encode and translate information in living systems, DNA and RNA, exhibit distinctive structural asymmetries, including homochirality or mirror image asymmetry and $3' - 5'$ directionality, that are invariant across…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…

We present a modular DNA origami design approach to address the challenges of assembling geometrically complex nanoscale structures, including those with nonuniform Gaussian curvature. This approach features a core structure that completely…

A \emph{wheel} is a graph made of a cycle of length at least~4 together with a vertex that has at least three neighbors in the cycle. We prove that the problem whose instance is a graph $G$ and whose question is "does $G$ contains a wheel…

Molecule generation is central to a variety of applications. Current attention has been paid to approaching the generation task as subgraph prediction and assembling. Nevertheless, these methods usually rely on hand-crafted or external…

DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this…

DNA nanostructures are made using synthetic DNA strands, the sequences of which are designed such that they will self-assemble into the desired form by hybridization of complementary domains. Various structures and devices have been…

Developing construction methods of materials tailored for given applications with absolute control over building block placement poses an immense challenge. DNA-coated colloids offer the possibility of realising programmable self-assembly,…

We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a…

Graph structured data, specifically text-attributed graphs (TAG), effectively represent relationships among varied entities. Such graphs are essential for semi-supervised node classification tasks. Graph Neural Networks (GNNs) have emerged…

Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to…

We examine the capacity of the complementarity spectrum to distinguish non-isomorphic digraphs. We focus on the seven families with exactly three complementarity eigenvalues. Our findings reveal that in some, but not all families, any two…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…

The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…

The defect morphology is an essential aspect of the evolution of crystals' microstructure and its response to stress. Existing methods either only report defect concentration or characterize only some of the defect morphologies. The need…

Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small…

Theory of splicing is an abstract model of the recombinant behaviour of DNAs. In a splicing system, two strings to be spliced are taken from the same set and the splicing rule is from another set. Here we propose a generalised splicing (GS)…

Biomolecular graph analysis has recently gained much attention in the emerging field of geometric deep learning. Here we focus on organizing biomolecular graphs in ways that expose meaningful relations and variations between them. We…

We propose a novel graph-driven generative model, that unifies multiple heterogeneous learning tasks into the same framework. The proposed model is based on the fact that heterogeneous learning tasks, which correspond to different…

Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks, which is in contrast with advances in generative models for images and text. Is it…