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Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…
Graph neural networks (GNNs) have demonstrated success in modeling relational data, especially for data that exhibits homophily: when a connection between nodes tends to imply that they belong to the same class. However, while this…
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…
Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they…
We solve the problem of characteristic numbers of elliptic curves in any dimensional projective space The answers are given in the form of effective recursions. Many numerical examples are provided. A C++ program implementing all the…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a…
Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
An obstacle representation of a graph is a mapping of the vertices onto points in the plane and a set of connected regions of the plane (called obstacles) such that the straight-line segment connecting the points corresponding to two…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
We study the problem of experimental design for accurately identifying the causal graph structure of a simple structural causal model (SCM), where the underlying graph may include both cycles and bidirected edges induced by latent…