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Synthetic power grids enable secure, real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power…
EEG microstate analysis segments continuous brain electrical activity into brief, quasi-stable topographic configurations that reflect discrete functional brain states. Conventional approaches such as Modified K-Means operate directly in…
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids…
A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated…
A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness; computing shortest paths or geodesics yields measures of network connectivity that can…
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigenvectors of the graph Laplacian. One attractive application of ER is to point clouds, i.e. graphs whose…
Multipatterning is an essential decomposition strategy in electronic design automation (EDA) that overcomes lithographic limitations when printing dense circuit layouts. Although heuristic-based backtracking and SAT solvers can address…
We perform numerical simulations to study self-assembly of nanoparticles mediated by an elastic planar surface. We show how the nontrivial elastic response to deformations of these surfaces leads to anisotropic interactions between the…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
A conception of mobile edge generation (MEG) is proposed, where generative artificial intelligence (GAI) models are distributed at edge servers (ESs) and user equipment (UE), enabling joint execution of generation tasks. Various distributed…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
Edge learning (EL), which uses edge computing as a platform to execute machine learning algorithms, is able to fully exploit the massive sensing data generated by Internet of Things (IoT). However, due to the limited transmit power at IoT…
This paper introduces simple analytical formulas for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over…
Extreme weather events can cause widespread power outages and huge economic losses. Low-income customers are more vulnerable to power outages because they live in areas with poorly equipped distribution systems. However, existing approaches…
Elasticity ellipses or central ellipses have been long used in graphic statics to capture the elastic behaviour of structural elements. The paper gives a generalisation the concept both in dimensions and in the possibility of degenerate…
Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations…
In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of…
Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such…