Proves minimal crossing diagrams for specific spatial graphs.
problem Proving minimal crossing diagrams for spatial graphs.
method Analyzing adequate diagrams and replacing vertices and edges.
result All 1-vertex spatial graphs with adequate diagrams have minimal crossing number.
Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
problem Unknottability of spatial graphs by region crossing changes.
method Region crossing changes to switch over/under relations within regions of spatial graph diagrams.
result Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
Spatial graphs can be unknotted with region crossing changes.
problem Unknotted spatial graphs composed of theta-curves.
method Region crossing changes on regions of theta-curves.
result Spatial graphs of theta-curves can be unknotted.
Study examines how changing regions affects planar graphs.
problem Effect of region crossing change on planar trivalent graphs.
method Investigation of region crossing changes on planar trivalent graphs.
result Effect of region crossing change on planar trivalent graphs.
The paper studies how the crossing number of graphs changes with a specific transformation called ΔY-move.
problem Investigating how the crossing number of graphs changes under the ΔY-move transformation.
method Analyzing the behavior of crossing number under the ΔY-move transformation on complete graphs.
result For any natural number k, there exists a sequence of ΔY-moves that decreases the crossing number of a complete graph.
Graphs represent knot adjacency for n crossings.
problem Understanding adjacency relationships between knots.
method Defined a new graph Γn to represent n-adjacency. result Proved several results about the new graph Γn. Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
problem Understanding the relationship between unknotting numbers and crossing numbers of spatial embeddings of planar graphs.
method Analyzing specific examples of planar graphs and their spatial embeddings to find counterexamples.
result There exist planar graphs and their spatial embeddings where the unknotting number is greater than half the crossing number.
Cross-GCN models cross features in GCN for better performance.
problem GCN's lack of cross feature modeling limits its effectiveness.
method Introduces Cross-feature Graph Convolution (Cross-GCN) to model cross features explicitly.
result Explicit cross feature modeling improves GCN's performance on tasks requiring cross features.
Graph cross network improves graph classification accuracy.
problem Improving graph classification accuracy.
method Graph cross network (GXN) with vertex infomax pooling (VIPool) and feature-crossing layer.
result Improves graph classification accuracy by 2.12% and 1.15%.
Study on crossing numbers of composite knots and graphs.
problem Understanding the minimal crossing number of composite knots and graphs.
method Relating the minimal crossing number of composite knots to the minimal crossing number of spatial graphs, specifically the 2n-theta curve.
result Proved that for large enough n, the crossing number of the 2n-theta curve is n times the sum of the crossing numbers of the prime knots.
SPX optimizes multiple graph drawing metrics for better readability.
problem Graph drawing algorithms often optimize one metric at a time, leading to suboptimal layouts.
method Introduces Stress-Plus-X (SPX) framework that optimizes stress, crossings, angles, and upwardness simultaneously.
result SPX achieves results close to state-of-the-art algorithms that optimize metrics individually.
The paper bounds crossing numbers of dense graphs on surfaces.
problem Estimating the minimum number of edge crossings for dense graphs on surfaces.
method Proved lower and upper bounds on crossing numbers, providing explicit families of surfaces.
result Upper and lower bounds on crossing numbers match up to constant factors.
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
problem Analyzing crossing and rotation numbers of cycles in plane immersions of graphs.
method Generic immersions and Legendrian embeddings of graphs, focusing on cycles of specific lengths.
result Sum of rotation numbers of all 5-cycles is even, and sum of crossing numbers is odd.
A graph G is called "minimalizable" if a diagram with minimal crossing number can be obtained from an arbitrary diagram of G by crossing changes. If, furthermore, the minimal diagram is unique up to crossing changes then G is called "strongly minimalizable". In this article, it is explained how minimalizability of a gr…
Unified interpretation of softmax cross-entropy and negative sampling for knowledge graph embedding.
problem Lack of theoretical relationship between softmax cross-entropy and negative sampling loss functions in knowledge graph embedding.
method Used Bregman divergence to provide a unified interpretation of the two loss functions.
result Theoretical findings for fair comparison of softmax cross-entropy and negative sampling are derived.
Optimal diagram found for complete graphs with linear trees.
problem Finding optimal diagrams for complete graphs.
method Using a linear tree structure to minimize crossing numbers.
result Optimal diagrams without free hamiltonian cycles for odd n≥7. In a recent work of Ayaka Shimizu[5], she defined an operation named region crossing change on link diagrams, and showed that region crossing change is an unknotting operation for knot diagrams. In this paper, we prove that region crossing change on a 2-component link diagram is an unknotting operation if and only…
Study calculates site-specific Gordian distances between graph embeddings.
problem Determining the minimal number of crossing changes between graph embeddings.
method Covering space theory for proofs.
result Site-specific Gordian distances between Milnor links and trivial links are determined.
DMGE learns cross-domain user behavior embeddings using multi-graphs and GNNs.
problem Data sparsity in learning large-scale item embedding from individual domain data.
method Construct multi-graphs from users' behaviors across domains, use multi-graph neural networks to learn cross-domain representation.
result DMGE outperforms state-of-the-art embedding methods in various tasks.
Proposes a novel approach using vector cross product to preserve directional edges in directed graphs.
problem Preserving directional edges in directed graphs for tasks like link prediction and node recommendation.
method Integrates the non-commutative property of vector cross product into a Siamese neural network to learn N-dimensional embeddings.
result Low-dimensional embeddings effectively preserve directional properties and outperform state-of-the-art methods.
New upper bound found for arc index of spatial graphs.
problem Finding an upper limit for the arc index of spatial graphs.
method Extended the definition of arc presentation to spatial graphs and derived a new upper bound.
result The upper bound on the arc index of any spatial graph is lowest possible.
Paper uses bipartite graph to forecast cross-market returns, revealing asymmetry.
problem Cross-market return predictability and asymmetry between U.S. and Chinese markets.
method Directed bipartite graph capturing time-ordered linkages, hypothesis testing for edge selection, regularized and ensemble machine learning models.
result U.S. returns predict Chinese intraday returns, but not vice versa, revealing asymmetry.
Study unknotting numbers of prime θ-curves up to 7 crossings.
problem Determine unknotting numbers for prime θ-curves.
method Subadditivity of unknotting numbers, non-overlapping set analysis, crossing changes, new methods for obstructing unknotting number 1.
result Exact unknotting numbers for all prime θ-curves up to 7 crossings.
XIMP improves molecular property prediction by integrating multiple graph representations.
problem Graph neural networks struggle in data-scarce regimes and fail to surpass traditional methods.
method Cross-graph inter-message passing with multiple graph abstractions.
result XIMP outperforms state-of-the-art baselines across diverse molecular property tasks.
NTKs explain GNNs' alignment for graph prediction.
problem Understanding GNNs' alignment for graph prediction.
method Analyzing NTKs and alignment in GNNs, focusing on cross-covariance.
result Optimizing alignment in GNNs optimizes graph representation.
GWCA analyzes cross-graph correlations for movie retrieval.
problem Cross heterogeneous graph comparison in movie retrieval.
method Spectral graph filtering, Wasserstein metric learning, generalized eigenvalue decomposition.
result Surprise consistency in learning processes and closed-form solution.
This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poinca…
Study on knot properties, showing relation between unknotting and crossing numbers.
problem Relations between unknotting and crossing numbers of spatial embeddings.
method Analyzes handcuff-graphs and theta curves, extends known results to handlebody-knots.
result Characterizes handlebody-knots satisfying the equality between unknotting and crossing numbers.
Predict stock movement by considering cross effects among stocks.
problem Challenges in predicting stock price movement due to cross effects among stocks.
method Multi-GCGRU framework combining GCN and GRU, encoding cross effects from financial domain knowledge and data-driven relationships.
result Our model outperforms other baselines in predicting stock movement.
G5 universal GRAPH-BERT learns graph representations across different datasets.
problem Learning graph representations across diverse graph datasets with distinct input and output configurations.
method G5 introduces a pluggable model architecture with input and output components for each graph data source, connected via a unified layer and fusion layer.
result G5 removes obstacles for cross-graph representation learning and transfer, even for sparse data.
Proposes MGMN for end-to-end graph similarity learning.
problem Lack of cross-level interactions in graph similarity learning.
method Multi-level graph matching network (MGMN) combining node-graph matching and siamese graph neural networks.
result MGMN outperforms state-of-the-art models on graph-graph classification and regression tasks.
A new invariant for complex knots and graphs using rational tangles.
problem Defining and analyzing complex knots and graphs with missing crossing information.
method Introducing a topological invariant using rational tangles to represent missing crossings or vertices.
result A compact invariant schema for pseudoknots, singular knots, and rigid vertex spatial graphs.
We study rerouting edges on surfaces without crossings.
problem Reconfiguring edge paths on surfaces without crossing.
method Rerouting one edge at a time, maintaining crossing-free intermediate embeddings.
result Reconfiguration is always possible on the torus and any orientable surface of genus at least one.
A new framework pretrains a single GNN model for diverse graphs, overcoming domain-specific challenges.
problem Difficulty in generalizing across graphs from different domains using existing GNNs.
method Cross-domain pretraining framework with gating functions to choose experts for new graphs.
result Superior performance on link prediction and node classification tasks across various domains.
THGFM models dynamic relational systems with cross-type and temporal fusion.
problem Learning on temporal heterogeneous graphs with diverse node and relation types.
method Dual-Path Architecture with Shared-Space and Relational Type-Partitioned Temporal Attention.
result THGFM outperforms baseline models on academic graph benchmarks.
The study evaluates cross-modal knowledge fusion methods.
problem Combining knowledge from text, KGs, and images.
method Evaluation of different fusion methods using embeddings.
result Potential of cross-modal knowledge fusion.
Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.
The paper extends graph signatures to Klein graphs and foams, linking signatures to knot properties.
problem Extending graph signatures to Klein graphs and foams.
method Developed an analogy of Murasugi's bounds and used signatures to lower bound knot properties.
result Lower bounds on negative orbifold Euler characteristics and unknotting numbers.
We say that a link L1 is an s-major of a link L2 if any diagram of L1 can be transformed into a diagram of L2 by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knot…
Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mappe…
Polygonalisation complex models mapping class group, with geometric insights.
problem Geometric model for mapping class group.
method Cube complex construction, flip graph analysis, hyperplane families, crossing graph study.
result Generic surfaces have distinct polygonalisation complexes, with quasi-isometric crossing graphs.
New graphs found that can be drawn without crossing links.
problem Finding graphs that can be drawn without links crossing.
method Provided specific examples for each n≥14. result Infinite family of graphs linklessly embeddable and Tutte-4-connected.
Deep learning predicts drug prescriptions across global health records.
problem Predicting drug prescriptions in chronic disease patients.
method Adaptive cross-global attention graph kernel network with support vector machine.
result Model outperforms current methods in accuracy and interpretability.
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded graphs.
Polynomial-time algorithm finds short non-orientable loops intersecting graph edges up to 30 times.
problem Finding short non-orientable loops intersecting graph edges efficiently.
method Combining computational biology techniques with recent graph theory results.
result Existence of short canonical non-orientable systems of loops.
Study on factorizations of knot polynomials for up to 12 crossings.
problem Understanding factorizations of HOMFLY polynomials for knots and links.
method Computer analysis of knots up to 12 crossings; irreducibility criterion for 2-connected plane graphs.
result Found 17 non-trivial factorizations of knots with up to 12 crossings.
Proposes Equity2Vec for cross-sectional asset pricing.
problem Sub-optimal performance due to missing cross-sectional effects and heterogeneous data.
method End-to-end deep learning framework with Equity2Vec for graph-based interactions and all alpha sources.
result Outperforms state-of-the-art approaches in real-world stock market datasets.
Introduces PELP for graph-enhanced word embeddings.
problem Combining graph side-information into static word embeddings.
method Probabilistic embeddings using Laplacian priors.
result Unified and flexible approach to various embedding methods.