Related papers: Neutral Networks of Sequence to Shape Maps
We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e. the neutral networks associated to the structure…
The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are…
We have developed different network approaches to analyze complex patterns of frictional interfaces (contact area developments). Network theory is a fundamental tool for the modern understanding of complex systems in which, by a simple…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
We introduce the concept of matching connectivity as a notion of connectivity in graph admitting perfect matchings which heavily relies on the structural properties of those matchings. We generalise a result of Robertson, Seymour and Thomas…
We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that preserves both the…
Shapes of interacting RNA complexes are studied using a filtration via their topological genus. A shape of an RNA complex is obtained by (iteratively) collapsing stacks and eliminating hairpin loops. This shape-projection preserves the…
A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which…
Graph are a ubiquitous data representation, as they represent a flexible and compact representation. For instance, the 3D structure of RNA can be efficiently represented as $\textit{2.5D graphs}$, graphs whose nodes are nucleotides and…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
We study noncrossing geometric graphs and their disjoint compatible geometric matchings. Given a cycle (a polygon) P we want to draw a set of pairwise disjoint straight-line edges with endpoints on the vertices of P such that these new…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
A full-homomorphism between a pair of graphs is a vertex mapping that preserves adjacencies and non-adjacencies. For a fixed graph $H$, a full $H$-colouring is a full-homomorphism of $G$ to $H$. A minimal $H$-obstruction is a graph that…
We describe two constructions of (very) dense graphs which are edge disjoint unions of large {\em induced} matchings. The first construction exhibits graphs on $N$ vertices with ${N \choose 2}-o(N^2)$ edges, which can be decomposed into…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to…