Related papers: Interaction Graphs: Graphings
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
This paper is an introduction to the language of Feynman Diagrams. We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable…
Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
Human beings are fundamentally sociable -- that we generally organize our social lives in terms of relations with other people. Understanding social relations from an image has great potential for intelligent systems such as social chatbots…
This article presents a survey of work on lifted graphical models. We review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We…
Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved),…
Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We formalise the notion of connection between two vertex sets in terms of edge and vertex…
The adaptive processing of graph data is a long-standing research topic which has been lately consolidated as a theme of major interest in the deep learning community. The snap increase in the amount and breadth of related research has come…
We introduce a new model of proteins, which extends and enhances the traditional graphical representation by associating a combinatorial object called a fatgraph to any protein based upon its intrinsic geometry. Fatgraphs can easily be…
Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce…
These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why…
Graphical modelling has a long history in statistics as a tool for the analysis of multivariate data, starting from Wright's path analysis and Gibbs' applications to statistical physics at the beginning of the last century. In its modern…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…
We survey the relationship between the combinatorics and geometry of graphs and the algebraic structure of right-angled Artin groups. We concentrate on the defining graph of the right-angled Artin group and on the extension graph associated…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…
Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…