相关论文: On phase in scaled graphs
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we…
Transformers have demonstrated success in graph learning, particularly for node-level tasks. However, existing methods encounter an information bottleneck when generating graph-level representations. The prevalent single token paradigm…
While Open Set Semantic Mapping and 3D Semantic Scene Graphs (3DSSGs) are established paradigms in robotic perception, deploying them effectively to support high-level reasoning in large-scale, real-world environments remains a significant…
We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases…
Signed graphs, which are characterized by both positive and negative edge weights, have recently attracted significant attention in the field of graph signal processing (GSP). Existing works on signed graph learning typically assume that…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
We put forward a novel method of constructing unfolded formulations of field theories, which is based on initial fixation of the form of an unfolded field and subsequent looking for the corresponding unfolded equation as an identity that…
We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…
We analytically explore the scaling properties of a general class of nested subgraphs in complex networks, which includes the $K$-core and the $K$-scaffold, among others. We name such class of subgraphs $K$-nested subgraphs due to the fact…
Given a signed social graph, how can we learn appropriate node representations to infer the signs of missing edges? Signed social graphs have received considerable attention to model trust relationships. Learning node representations is…
A signed graph product is defined for a new product, and initially the unsigned graph product's Laplacian spectrum and signless Laplacian spectrum are found. Next, for the signed graph product, the adjacency spectrum, Laplacian spectrum,…
In this article, we propose a novel navigation framework that leverages a two layered graph representation of the environment for efficient large-scale exploration, while it integrates a novel uncertainty awareness scheme to handle dynamic…
Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
The lattice gauge-scalar model with the scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase which is well-known as the Fradkin-Shenker-Osterwalder-Seiler analytic continuity theorem:…
Graph Transformer (GT) has recently emerged as a promising neural network architecture for learning graph-structured data. However, its global attention mechanism with quadratic complexity concerning the graph scale prevents wider…
Incorporating graphs in the analysis of multivariate signals is becoming a standard way to understand the interdependency of activity recorded at different sites. The new research frontier in this direction includes the important problem of…
In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…
A signed graph $\Gamma$ is said to be determined by its spectrum if every signed graph with the same spectrum as $\Gamma$ is switching isomorphic with $\Gamma$. Here it is proved that the path $P_n$, interpreted as a signed graph, is…