Characterizes lamination spaces of graphs on a pair of pants.
problem Understanding lamination spaces of graphs on a pair of pants.
method Identifying lamination spaces as lattice polytopes and using graph exploration technique.
result Characterizes the polytopes that arise as lamination spaces of graphs on a pair of pants.
We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g --> g^{-1}, h --> h^{-1} extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pa…
The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the co…
MTRGL learns temporal correlations from multi-modal data for improved pair trading.
problem Discerning temporal correlations among financial entities.
method Combines time series data and discrete features into a temporal graph, using a memory-based temporal graph neural network.
result MTRGL outperforms traditional methods in temporal graph link prediction and pair trading.
Improves molecular activity prediction using graph convolutional neural networks considering graph distances.
problem Predicting molecular activity using graph convolutional neural networks with improved distance representation.
method Proposed three improvements: modified graph distances, distance-dependent weight matrices, and weighted sum conversion.
result The proposed method slightly outperforms the original weave module in compound activity prediction.
Paper describes eigenvalues of genus 3 surfaces graphs.
problem Understanding eigenvalues of genus 3 surfaces.
method Analyzes graphs derived from pair of pants decompositions.
result Complete description of eigenvalue sets for genus 3.
We associate a two-step nilpotent Lie algebra to an arbitrary Schreier graph. We then use properties of the Schreier graph to determine necessary and sufficient conditions for this Lie algebra to extend to a three-step nilpotent Lie algebra. As an application, if we start with pairs of non-isomorphic Schreier graphs co…
Characterizes weakly linked pairs of complete graphs in 3D space.
problem Identifying pairs of complete graphs that are weakly linked.
method Algebraic characterisation and geometric analysis of linking cycles.
result Characterization of weakly linked pairs of complete graphs.
Graph Neural Networks solve topology problems in simple 3D models.
problem Deciding homeomorphism of 3-manifolds described by plumbing graphs.
method Supervised and reinforcement learning with Graph Neural Networks.
result High accuracy in determining homeomorphic 3-manifolds.
A new method improves graph node embeddings by considering both nearby and distant node similarities.
problem Improving graph node embeddings by considering both nearby and distant node similarities.
method Distance-aware Negative Sampling (DNS) which maximizes cohesion at nearby node-pairs and separation at distant node-pairs.
result DNS outperforms baseline methods in downstream node classification tasks on various datasets and GRL algorithms.
In this paper we enumerate and classify the ``simplest'' pairs (M,G) where M is a closed orientable 3-manifold and G is a trivalent graph embedded in M. To enumerate the pairs we use a variation of Matveev's definition of complexity for 3-manifolds, and we consider only (0,1,2)-irreducible pairs, namely pairs (M,G) suc…
The paper explores linked cycles in graphs and their properties.
problem Understanding the structure of linked cycles in graphs.
method Analyzing the set of all pairs of disjoint cycles in graphs and showing conditions for minimally linked sets.
result A minimally linked set of cycles in a complete graph Kp+q has at most eighteen elements. We investigate Legendrian graphs in (R3,ξstd). We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with tb=−1 and rot=0 if and only if it does not contain K4 as a mi…
GLSearch uses GNN to learn efficient search strategies for finding large common subgraphs.
problem Finding the Maximum Common Subgraph (MCS) between two graphs is NP-hard and hard to solve efficiently.
method GLSearch combines GNN and DQN to learn optimal node pairs for expansion in a branch and bound algorithm.
result GLSearch finds significantly larger common subgraphs than heuristic search methods given the same computation budget.
The study finds pairs of curves at distance 5 in surface curve graphs.
problem Finding pairs of curves at distance 5 in the curve graph of closed surfaces.
method Applying Dehn twists to fixed curves and characterizing conditions for distance 5.
result Characterization of pairs of curves at distance 5 in surface curve graphs.
Proves accuracy guarantees for self-supervised learning with correlated positive pairs.
problem Lack of theoretical guarantees for self-supervised learning with correlated positive pairs.
method Novel augmentation graph concept and spectral decomposition loss.
result Provably accurate features under linear probe evaluation.
Deep Divergence Graph Kernels learn graph representations without supervision.
problem Learning graph representations without feature engineering or labeled graphs.
method Unsupervised method using cross-graph attention networks and divergence scores.
result Learned representations achieve competitive results on graph classification tasks.
A novel graphical matching approach improves pairs trading by reducing portfolio variance and risk-adjusted returns.
problem Common pairs trading methods lead to high portfolio variance and low risk-adjusted returns due to focusing on highly cointegrated assets.
method Model all assets and their cointegration levels with a weighted graph. Select pairs as a maximum weighted matching to ensure no shared assets and lower portfolio variance.
result The matching-based strategy shows a significant improvement in risk-adjusted performance, with a gross Sharpe ratio of 1.23.
Characterizes ends and coends of graph pairs using quasi-median graphs.
problem Understanding the number of ends and coends in graph pairs.
method Characterizes ends and coends using quasi-median graphs.
result Characterizes ends and coends of graph pairs (G,H) in terms of quasi-median graphs. We define two new families of invariants for (3-manifold, graph) pairs which detect the unknot and are additive under connected sum of pairs and (-1/2)-additive under trivalent vertex sum of pairs. The first of these families is closely related to both bridge number and tunnel number. The second of these families is a …
Algorithm discovers edges between pairs of nodes with limited queries.
problem Discovering good matches between pairs of entities with limited queries.
method Pair-matching problem as a multi-armed bandit with constraints, focusing on Stochastic Block Model.
result Sublinear regret achievable in Stochastic Block Model with two communities, with phase transition related to community detection.
Let G be a graph in a 3-manifold M. We compress the pair (M,G) along admissible 2-spheres as long as possible. What we get is a root of (M,G). Our main result is that for any pair (M,G) the root exists and is unique. As a corollary we get an easy proof of Petronio's theorem on prime decompositions of 3-orbifolds.
Predicts unseen links in graphs using motifs of 3-5 nodes.
problem Predicting new links in graphs for various applications.
method Uses motifs of 3-5 nodes for link prediction, optimizing feature construction and negative example sampling.
result Higher classification accuracy compared to prior methods.
Paper detects non-trivial cycles in embedding spaces using graph integrals.
problem Detecting non-trivial cycles in embedding spaces.
method Construct cycles from chord diagrams, use modified configuration space integrals, and pair arguments.
result Non-trivial cycles in embedding spaces are detected.
This paper proposes a new method to learn combinatorial patterns for airline crew pairing optimization.
problem Enhancing airline crew pairing optimization for large-scale, complex flight networks.
method Variational Graph Auto-Encoder for learning combinatorial patterns among flight-connection graphs.
result The proposed method generates new pairings for the optimizer, improving the efficacy of airline crew pairing optimization.
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.
Graph Matching Networks learn graph similarity using GNN embeddings.
problem Learning similarity between graph structured objects.
method Graph Matching Network model using cross-graph attention mechanism.
result Models outperform baseline systems in function similarity search.
SIGMA model improves graph matching across various applications.
problem Graph matching problem in different domains.
method Stochastic Iterative Graph Matching (SIGMA) model with multi-step refinement and dummy nodes.
result SIGMA produces significantly improved graph matching results compared to state-of-the-art models.
Researchers analyze geodesic complexity in robot paths on tree graphs.
problem Understanding optimal paths for robots on tree graphs.
method Examined geodesic complexity in ordered and unordered configuration spaces of graphs in ℓ1 and ℓ2 metrics, finding explicit geodesics and families. result Geodesic complexity matches topological complexity in all cases studied.
Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P^2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning techniques are improved using a modification of the union-find alg…
Researchers identify critical protein residues using advanced graph theory.
problem Identifying essential residues in proteins for function.
method Learning Random Geometric Graphs (RGG) with Cramer's V correlation and organic thresholding.
result Advanced RGG methods accurately identify critical residues compared to existing techniques.
Study examines persistence diagrams in machine learning, proposing permutation tests.
problem Understanding the power and limitations of persistence diagrams in machine learning.
method Carried out experiments on graph and shape data, proposed permutation tests for persistence diagrams.
result Persistence pairing shows significant improvement in various tasks, but the most critical values are most discriminative.
Develops structured noise for more accurate graph classifier robustness certificates.
problem Isotropic noise limits robustness certificates for graph classifiers.
method Randomized smoothing with anisotropic noise distribution.
result Structured-aware robustness certificates provide more accurate predictions.
LC-GNN improves GNNs for node classification by incorporating label consistency.
problem Limited performance of GNNs due to label consistency assumption not always holding.
method LC-GNN uses node pairs with the same label but unconnected to expand GNN's receptive field.
result LC-GNN outperforms traditional GNNs in semi-supervised node classification.
PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.
problem Efficiently compute graph similarity scores for large graphs.
method Graph partitioning followed by subgraph-level and node-level comparisons using a graph neural network.
result PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks.
Improved KG completion on large datasets using entity-relation pair occurrences.
problem Performance bottleneck in training large-scale KGs due to memory constraints.
method Construct a joint learning model using pairwise occurrence information and increase negative sampling quality.
result Significant improvement in performance, especially with low batch size and negative examples.
The study finds surface subgroups in specific types of groups.
problem Finding surface subgroups in certain groups.
method Analyzing graph pairs and using properties of fundamental groups and limit groups.
result Surface subgroups found in graph pairs and limit groups.
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time enumeration. However, asymptotically most graphs do not result in …
New spectral conditions ensure graph rigidity and global rigidity in the Euclidean plane.
problem Ensuring graph rigidity and global rigidity in the Euclidean plane.
method Improving algebraic connectivity bounds for graph rigidity and global rigidity.
result Every 6-connected graph is rigid and globally rigid if its algebraic connectivity exceeds specific thresholds.
HighwayGraph models long-distance node relations in GNNs with improved performance.
problem Limited-layer information propagation in GNNs hinders long-distance node relation modeling.
method Proposes two solutions: implicit and explicit modeling of long-distance node relations using shallow GNN architectures and a self-training framework.
result HighwayGraph achieves consistent and significant improvements over four GNNs on three benchmark datasets.
Proposes a new method for predicting missing relations in knowledge graphs.
problem Predicting missing relations between entities in knowledge graphs.
method Relational message passing method considering only edge features without entity IDs.
result PathCon method outperforms state-of-the-art methods significantly.
PAIR-CI calibrates CI tests for causal discovery with incomplete data.
problem Miscalibration of CI tests when imputing incomplete data.
method Integrates multiple imputation directly into the inferential procedure via a paired permutation design.
result PAIR-CI reduces false positive rates to below 5% in simulations.
Study on linking numbers in random book embeddings of complete graphs.
problem Distribution and mean of linking numbers in random book embeddings of complete graphs.
method Analyzes a family of two-component links arising from random embeddings of complete graphs, using Eulerian numbers and linear growth in mean linking number.
result Mean of squared linking number over all random embeddings is $ rac{i}{6}$, where i is the number of interior edges. Characterizes groups with specific boundary properties.
problem Groups with Schottky set boundaries.
method Study relatively hyperbolic group pairs with Schottky boundaries.
result Groups with boundaries where Schottky sets have 1 or 2 component incidence graphs.
The question of aggregating pair-wise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR's TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In mo…
A theory of complexity for pairs (M,G) with M an arbitrary closed 3-manifold and G a 3-valent graph in M was introduced by the first two named authors, extending the original notion due to Matveev. The complexity c is known to be always additive under connected sum away from the graphs, but not always under connected s…
Motivated by his studies in knot theory V. Vassiliev introduced X-graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which X-graph can be embedded into a plane respecting the the X-structure at every vertex. The conjecture was proved by…
New chiral minimal surfaces derived from quartz network.
problem Finding new triply-periodic minimal surfaces.
method Using dual graphs of quartz and its dual, generating area-minimizing meshes, and identifying flat point structures.
result Identified a new family of chiral triply-periodic minimal surfaces.