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.
New graph shows edge deletion/contraction doesn't always result in intrinsically linked graphs.
This paper classifies chiral graphs up to size 12.
Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation learning on graphs in general. As the developed methodologies become more sophistic…
ELD compares graphs by their embedded Laplacian eigenvectors, resolving ambiguities.
We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.
Automorphisms of fine 1-curve graph linked to surface homeomorphisms.
The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.
The maximum number of maximum cliques in a graph is determined for graphs with at least 15 vertices.
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed…
GraphACL learns graph representations without augmentation or homophily assumptions.
Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged as powerful node embedding methods, with promising performances on challenging tasks such as link prediction and node clustering. Graph AE, VAE and most of their extensions rely on graph convolutional networks (GCN) to learn vector space repres…
Random subsurfaces of hyperbolic surfaces equidistribute to ribbon graphs.
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over the graph. When applying the proximal gradient algorithm to solve this problem, t…
The paper examines deformations of simple dotted graphs made of circles.
Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tenso…
Rotation systems can't always be drawn in surfaces.
The paper calculates graph Ricci curvature and finds properties of specific graph types.
Connected graph for twice-punctured torus curves.
New method to classify simple Smale flows on .
Study Morse functions on projective plane using Reeb graphs.
Machine learning techniques have recently been adopted in various applications in medicine, biology, chemistry, and material engineering. An important task is to predict the properties of molecules, which serves as the main subroutine in many downstream applications such as virtual screening and drug design. Despite th…
Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective strengths and weaknesses. However, most of them rely on complex mathematics and requir…
New algorithms learn simple staged trees from data, improving model fit.
New non-homophilous graph datasets and methods for scalable learning.
Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.
Simple Euclidean models outperform hyperbolic graph learning models.
Graph Neural Networks solve topology problems in simple 3D models.
A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigz…
In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the -separation criterion. These include MC, summary, and ancestral grap…
Determinants of theta curves and symmetric graphs are studied.
We present RL-VAE, a graph-to-graph variational autoencoder that uses reinforcement learning to decode molecular graphs from latent embeddings. Methods have been described previously for graph-to-graph autoencoding, but these approaches require sophisticated decoders that increase the complexity of training and evaluat…
Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is di…
We prove a Reeb sphere theorem for finite simple graphs. The result bridges two different definitions of spheres in graph theory. We also reformulate Morse conditions in terms of the center manifolds, the level surface graphs {f=f(x)} in the unit sphere S(x). In the Morse case these graphs are either spheres, the empty…
The paper studies actions on Bass-Serre trees and identifies new -simple groups.
Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been pro…
Classifies graph configuration spaces homeomorphic to manifolds.
We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the graphs from which they arise are isomorphic.
SASE improves attributed graph clustering for large graphs with linear time and space complexity.
Explains partial duality for ribbon graphs in simple terms.
Refines Ozsváth-Szabó d-invariants for knot concurrence.
In the present paper we construct a one-to-one correspondence between the set of graph-knots and the set of homotopy classes of looped graphs. Moreover, the graph-knot and the homotopy class constructed from a given knot are related with this correspondence. This correspondence is given by a simple formula.
We show that for any simple non-oriented graph G with at least thirteen vertices either G or its complement is intrinsically linked.
Seminal works on graph neural networks have primarily targeted semi-supervised node classification problems with few observed labels and high-dimensional signals. With the development of graph networks, this setup has become a de facto benchmark for a significant body of research. Interestingly, several works have rece…
We present a graph manifold analog of the Jankins-Neumann classification of Seifert fibered spaces over admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for any graph manifold with torus boundary. As an application of a generalization of this result to F…
We prove that the expectation value of the index function i(x) over a probability space of injective function f on any finite simple graph G=(V,E) is equal to the curvature K(x) at the vertex x. This result complements and links Gauss-Bonnet sum K(x) = chi(G) and Poincare-Hopf sum i(x) = chi(G) which both hold for arbi…
The ability of a graph neural network (GNN) to leverage both the graph topology and graph labels is fundamental to building discriminative node and graph embeddings. Building on previous work, we theoretically show that edGNN, our model for directed labeled graphs, is as powerful as the Weisfeiler-Lehman algorithm for …
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many s…
The paper encloses computation of simple centralizer of simple braids and their connection with Fibonacci numbers. Planarity of some commuting graphs is also discussed in the last section.