As the availability and importance of temporal interaction data--such as email communication--increases, it becomes increasingly important to understand the underlying structure that underpins these interactions. Often these interactions form a multigraph, where we might have multiple interactions between two entities.…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
28 results for “multigraphs”
The study proves planes are the only complete uniformly elliptic Weingarten multigraphs.
problem Proving planes are the only complete uniformly elliptic Weingarten multigraphs.
method Proving planes are the only complete multigraphs with quasiconformal Gauss map and bounded second fundamental form.
result Proves planes are the only complete uniformly elliptic Weingarten multigraphs.
Classifies multigraphs for torus actions on 6D manifolds with isolated fixed points.
problem Classifying torus actions on 6D manifolds with isolated fixed points.
method Associate multigraphs to fixed point data, study operations, and prove classification.
result Classifies multigraphs for 6D manifolds by converting them into the empty graph.
Proposes a new method to optimize graph neural network architectures on heterogeneous information networks.
problem Weaknesses in instability and inflexibility of existing graph neural architecture search methods.
method Partial Message Meta Multigraph search (PMMM) using a differentiable framework to search for a meaningful meta multigraph.
result Significantly more stable and effective than state-of-the-art heterogeneous GNNs.
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for mathematicians, constructing them is difficult: the best algorithms to date have not gone beyond n = 12. The underlying algorithms essential…
Study circle actions on unitary manifolds with discrete fixed points.
problem Understanding circle actions on compact unitary manifolds with discrete fixed points.
method Prove relationships between weights at fixed points and derive results regarding the first equivariant Chern class and Hirzebruch -genus.
result Derive a multigraph encoding fixed point data, leading to new insights into unitary -manifolds.
MGMC method handles missing data in medical datasets for accurate disease classification.
problem Handling missing data in incomplete medical datasets for accurate disease classification.
method Multigraph Geometric Matrix Completion (MGMC) using multiple graph convolutional networks.
result MGMC achieves superior classification and imputation performance compared to state-of-the-art approaches.
In this paper, we study a circle action on a compact oriented manifold with a discrete fixed point set. The fixed point data consists of the weights of the -representations at the fixed points. We prove various results and properties of the action, in terms of the fixed point data. We show that the manifold can be…
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address thi…
We study the problem of end-to-end learning from complex multigraphs with potentially very large numbers of edges between two vertices, each edge labeled with rich information. Examples range from communication networks to flights between airports or financial transaction graphs. We propose Latent-Graph Convolutional N…
New models capture heterogeneous network density, improving community detection.
problem Empirical networks are often globally sparse but locally dense.
method Latent Poisson models generating hidden multigraphs.
result These models improve community detection in sparse networks.
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a piecewise constant estimation of the density of the edges across the clusters, and ad…
Constructs polyhedral chains with prescribed tangent plane distributions.
problem Constructing polyhedral chains with specific tangent plane distributions.
method Explicit construction of polyhedral chains that approximate prescribed measures on Grassmannian.
result Polyconvexity is equivalent to quasiconvexity of associated Q-integrands under certain conditions.
We proposed a probabilistic approach to joint modeling of participants' reliability and humans' regularity in crowdsourced affective studies. Reliability measures how likely a subject will respond to a question seriously; and regularity measures how often a human will agree with other seriously-entered responses coming…
We prove that any complete surface with constant mean curvature in a homogeneous space E(κ,τ) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a consequence we get that any orientable, parabolic, complete, immersed surface with constant mean curvature H in E(κ,τ) (different fr…
Study shows how many crossings arise in curves on surfaces.
problem Understanding crossings in curves on surfaces.
method Proved a minimum crossing number growth rate for curves.
result Effective bounds with optimal growth rates on every orientable surface.
Fatgraphs are multigraphs enriched with a cyclic order of the edges incident to a vertex. This paper presents algorithms to: (1) generate the set of all fatgraphs having a given genus and number of boundary cycles; (2) compute automorphisms of any given fatgraph; (3) compute the homology of the fatgraph complex. The al…
Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured, nonparametric edge-exchangeable graphs. However, such exchangeable models necessarily ig…
A Spectral Bernstein Theoremmath.DG
We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface in . (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that has only essential spectrum consisting of the half line . This is t…
The paper studies almost complex torus manifolds using graphs and Hirzebruch genera, proving properties of their fixed points and cohomology.
problem Understanding the fixed points and cohomology of almost complex torus manifolds.
method Using directed labeled multigraphs and Hirzebruch genera to encode and analyze the manifolds.
result Almost complex torus manifolds have positive Todd genus and at least n+1 fixed points.
A maximal surface $\sb$ with isolated singularities in a complete flat Lorentzian 3-manifold is said to be entire if it lifts to a (periodic) entire multigraph $\tilde{\sb}$ in In addition, $\sb$ is called of finite type if it has finite topology, finitely many singular points and $\tilde{\sb}$ is finitely …
Study on minimal surfaces in a specific homogeneous space with non-existence and construction results.
problem Minimal surfaces in with asymptotic boundary conditions.
method Non-existence proofs and construction of specific minimal surfaces.
result Existence and non-existence results for minimal surfaces in .
I answer an open question left by Gui-Song Li in "On self-intersections of immersed surfaces" (AMS Proceedings, Volume 126, 1998, pp.3721-3726.) The intersection graph of a generic surface is the set of values which are either singularities or intersections. It is a multigraph whose edges are trans…
The paper explores holonomy, zeta functions, and cohomology in foliated manifolds with stratified boundaries.
problem Understanding symmetries and cohomology in foliated manifolds with stratified boundaries.
method Developed a novel formalism for the Gamma-set and defined an Ihara zeta function to encode symmetries. Investigated the relationship between holonomy and zeta functions, and analyzed how the twist map impacts cohomology.
result Conjectured a duality between holonomy fixed points and the poles of the Ihara zeta function, extending to twisted cohomology classes.
Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As real-world graphs are often incomplete and noisy, treating them as ground-truth inform…
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population genetics, ecology or network analysis. While the exchangeability assumption is sensib…
Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with the pairwise comparisons. Our goal in this paper is to develop a method …
ProGraML uses graph-based machine learning to improve program optimization and analysis.
problem Improving program optimization and analysis with machine learning.
method Low-level, language agnostic graph representation and message passing neural networks.
result ProGraML achieves an average 94.0 F1 score on a benchmark dataset, significantly outperforming state-of-the-art approaches.