Related papers: Mass generation in graphs
Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose \HEDGE,…
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods.…
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state.…
Traditionally, Quantum Field Theory (QFT) treats particle excitations as point-like objects, which is the source of ubiquitous divergences. We demonstrate that a minimal modification of QFT with finite volume particles may cure QFT of…
The interaction between the complex antisymmetric tensor matter field and a scalar field is constructed. We analyze the Higgs mechanism and show the generation of mass and topological terms by spontaneous symmetry breaking.
An attempt to evade the strict uniqueness of consistent interactions involving spin-2 particles is made by modifying the Noether procedure from the outset. A vector field is introduced, coupled to a graviton already at the level of…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
In this paper we study weighted distances in scale-free spatial network models: hyperbolic random graphs (HRG), geometric inhomogeneous random graphs (GIRG) and scale-free percolation (SFP). In HRGs, $n=\Theta(\mathrm{e}^{R/2})$ vertices…
Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…
In this paper we investigate phenomena of spontaneous emergence or purposeful formation of highly organized structures in networks of related agents. We show that the formation of large organized structures requires exponentially large, in…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning,…
\begin{abstract} In this paper, we investigate a shift arising from graph $G$. We prove that any $k$-dimensional shift of finite type can be generated through a $k$-dimensional graph. We investigate the structure of the shift space using…
In clouds of suspended particles (grains, droplets, spheres, crystals, etc.), collisions electrify the particles and the clouds, producing large electric potential differences over large scales. This is seen most spectacularly in the…
Graphs are used to represent and analyze data in domains as diverse as physics, biology, chemistry, planetary science, and the social sciences. Across domains, random graph models relate generative processes to expected graph properties,…
This study presents a novel algorithm based on graph theory for the precise segmentation and measurement of detonation cells from 3D pressure traces, termed detonation lattices, addressing the limitations of manual and primitive 2D edge…
We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…