New algebraic structures biquasiles defined using dual graph diagrams for knot and link invariants.
problem Defining invariants for oriented knots and links.
method Introducing dual graph diagrams and biquasiles, using combinatorial and algebraic approaches.
result Defined new knot and link invariants using biquasiles.
Dual-Primal Graph CNN learns vertex and edge features on graphs.
problem Learning features on non-Euclidean structured data like graphs.
method Alternates graph convolutional operations on graph and its dual.
result State-of-the-art results on various graph benchmarks.
Accelerated Gibbs sampling for Gaussian graphical models using dual factor graphs.
problem Improving convergence rate of Gibbs sampling for Gaussian graphical models.
method Dual normal factor graph approach to accelerate convergence.
result Universal convergence rate improvement in dual domain for all homogeneous models.
Paper categorifies a polynomial related to ribbon graphs.
problem Enumerating partial duals of ribbon graphs.
method Using an extended Frobenius algebra in unoriented topological quantum field theory.
result A categorification of the partial-dual genus polynomial.
Dual CNN for predicting links in graphs of graphs.
problem Link prediction in graphs of graphs.
method Dual Convolutional Neural Network (CNN) for combining external and internal graph structures.
result Effective link prediction on chemical network datasets.
The paper extends NUP representations to factor graphs for better estimation.
problem Nontrivial model-based estimation problems.
method Augmenting factor graphs with convex-dual variables and NUP representations; proposing a new iterative algorithm.
result A new dual algorithm for state space problems.
Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to gluings of higher dimensional simplices. It is generally assumed that GFT graphs are always dual to pseudo manifolds. In this paper we prove that already in dimension three (and in all higher dimensions), this is not true due…
We prove a mapping between dual and primal factor graph marginals for efficient estimation.
problem Efficient estimation of marginal densities in factor graphs.
method Local mappings derived from Fourier transforms of local factors, applied to Ising and Potts models.
result Marginal densities can be more accurately estimated in the dual domain.
Smooth manifolds can be triangulated with graphs of bounded twin-width.
problem Understanding the structure of triangulations of smooth manifolds.
method Using Whitney's triangulation method and bounding the twin-width of specific graphs.
result Compact smooth manifolds have triangulations with graphs of bounded twin-width.
Dual-attention GCN improves text classification by adapting to textual complexity.
problem Challenges in learning discriminative features from texts due to graph variants.
method Proposes a dual-attention GCN with connection-attention and hop-attention mechanisms.
result Achieves state-of-the-art performance on text classification tasks.
In this note, I discuss in some detail the dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in math.AG/0402015, and used in math.QA/0412149 to construct open-closed topological conformal field theories. This dual version of the r…
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.
We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobas-Riordan polynomials of dual graphs. This relation unifies various recent results expressing the J…
Dual regularized graph Laplacian improves spectral clustering for community detection.
problem Detecting clusters in networks with improved spectral clustering methods.
method Proposes dual regularized graph Laplacian for three spectral clustering approaches.
result Theoretical analysis shows DRSC and DRSLIM yield stable consistent community detection.
MR-GNN predicts interactions between structured entities using multi-resolution and dual graph neural networks.
problem Predicting interactions between structured entities, especially considering features in substructures of different sizes and interactions between entities.
method MR-GNN uses a multi-resolution architecture and dual graph-state L-STMs to extract features from different neighborhoods and pairwise graphs, respectively.
result MR-GNN improves prediction accuracy compared to state-of-the-art methods.
FairDTD improves fairness in GNNs by distilling dual teacher knowledge, balancing utility and bias.
problem Bias in GNN predictions due to sensitive attributes.
method Dual-Teacher Distillation with a causal graph model, feature and structure teachers, and graph-level distillation.
result Achieves optimal fairness while preserving high model utility.
CADE learns dual node representations for better generalization.
problem Transductive graph embeddings cannot generalize to unseen nodes or across different graphs.
method CADE combines real-time neighborhoods with neighbor-attentioned representation, preserving known node memory.
result CADE outperforms state-of-the-art methods in generalization and context-awareness.
PDNAS optimizes GNN architectures for diverse datasets.
problem Inadequate adaptability and combinatorial search space in GNNs.
method Dual architecture search (micro- and macro-architectures) with gradient-based optimization.
result PDNAS finds deeper GNNs with better performance on diverse datasets.
Dual-edge spatial Jacobian image graph for interpretable diabetic retinopathy grading
problem Automated diabetic retinopathy grading from color fundus photographs
method Dual-edge spatial-Jacobian image graph
result 0.8076 accuracy, 0.8312 quadratic weighted kappa, 0.5915 macro-F1, 0.9330 adjacent-grade accuracy
Convex optimization method infers latent structure in random dot product graphs.
problem Inferring latent probability matrix of random dot product graphs.
method Conic programming with nuclear norm regularization.
result Asymptotic consistency of probability estimates and recovery of latent structure.
The main results in this paper provide upper bounds of the second order Dehn functions for three-dimensional groups Nil and Sol. These upper bounds are obtained by using the Varopoulos transport argument on dual graphs. The first step is to start with reduced handlebody diagrams of the three-dimensional balls either im…
The paper introduces curvature-based clustering algorithms for graph analysis.
problem Identifying densely connected substructures in graphs for community detection.
method Discrete Ricci curvatures and geometric flows to reveal community structure.
result The curvature-based approach can identify overlapping communities in graphs.
Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.
problem Efficient estimation of marginal probabilities in statistical physics models.
method Local mappings based on Fourier transform of local factors, applied to Ising, Potts, and clock models.
result Local extrema of fixed points are at phase transition points, and the mapping facilitates efficient estimation.
This paper improves upper bounds on ribbonlength for certain alternating links.
problem Finding tighter bounds on the ribbonlength of alternating links.
method Proved a new upper bound for alternating links with bipartite dual graphs.
result Improved upper bounds on ribbonlength for specific links.
In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general r…
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
engGNN combines external and generated graphs to improve disease classification and biomarker discovery.
problem Challenges in integrating omics data due to high dimensionality and small sample sizes.
method Dual-graph framework that integrates external biological networks with data-driven generated graphs.
result engGNN outperforms state-of-the-art methods in disease classification and biomarker discovery.
A new online learning algorithm for graph-structured sparsity.
problem Efficiently handling graph-structured sparsity constraints in online learning settings.
method Proposes extsc{GraphDA} algorithm that projects gradients and variables onto subspaces.
result Improves classification performance and captures graph-structured features effectively.
DAGCN improves graph classification by learning neighbor importance and pooling.
problem Loss of early-stage information and loss of node characteristics in GCNs.
method Dual attention graph convolution and self-attention pooling.
result DAGCN outperforms state-of-the-art methods in graph classification.
The study connects geodesic flows on Riemann surfaces to random walks on their dual graphs.
problem Understanding ergodicity of geodesic flows on infinite Riemann surfaces.
method Analyzing random walks on the dual graph of pants decompositions.
result Equivalence between ergodicity of geodesic flows and recurrence of random walks.
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.
A formula calculates the Euler class of foliations using dual graphs.
problem Calculating the Euler class of foliations using cooriented branched surfaces.
method Using dual graphs of cooriented branched surfaces to define a simplicial 1-cycle representing the Poincaré dual of the Euler class.
result The formula generalizes previous results and classifies realizable homology classes.
Entire minimal graphs in Heisenberg space have negative Gauss curvature.
problem Characterizing entire minimal graphs in Heisenberg space.
method Defining holomorphic quadratic differentials and using them to describe entire graphs.
result Entire minimal graphs in Heisenberg space have negative Gauss curvature.
Study classifies Morse functions with 4 critical points on immersed 2-spheres.
problem Classifying Morse functions with 4 critical points on immersed 2-spheres.
method Used dual graph of immersion and Reeb graphs to classify functions.
result Found all possible structures of the functions.
Dual-based algorithms optimize distributed convex problems over networks.
problem Optimizing distributed convex problems over network constraints.
method Dual formulation of primal problem, distributed algorithms achieving optimal rates.
result Achieves optimal rates similar to centralized algorithms with additional cost related to network spectral properties.
DanSmp predicts stock movement using a hybrid-relational MKG and dual attention networks.
problem Predicting stock price trends in volatile financial markets.
method Constructs a bi-typed MKG with hybrid-relations and uses DanSmp, a dual attention network, to learn momentum spillover signals.
result DanSmp improves stock prediction accuracy using the MKG.
We consider an embedding of a 2-dimensional CW complex into the 3-sphere, and construct it's dual graph. Then we obtain a homogeneous system of linear equations from the 2-dimensional CW complex in the first homology group of the complement of the dual graph. By checking that the homogeneous system of linear equa…
SBO uses dual voting to build consensus in noisy feedback settings.
problem Collective decision-making under social influence.
method Dual voting system with noisy public votes and private interviews.
result Efficient consensus-building through noisy public votes, debiased by estimated social graph.
The article studies embeddings of edge-colored graphs related to balanced 3- and 4-manifolds.
problem Investigating embeddings of edge-colored dual graphs of balanced 3- and 4-manifolds.
method Introducing the concept of balanced genus and proving lower bounds for the genus of 3- and 4-manifolds.
result Established lower bounds for the balanced genus of 3- and 4-manifolds, and conditions for homeomorphism to spheres.
Method uses TV minimization for semi-supervised learning on network data.
problem Semi-supervised learning from partially-labeled network data.
method Graph signal recovery interpretation, total variation minimization, primal-dual method for non-smooth convex optimization.
result TV minimization recovers clusters in the empirical graph of the data under certain network conditions.
Optimizes wireless network resource management with state-augmented policies.
problem Optimizing network-wide utility with user performance constraints.
method State-augmented parameterization of RRM policy, using dual variables.
result Superior trade-off between mean, minimum, and 5th percentile rates.
Graph neural networks optimize radio resource management policies for wireless networks.
problem Optimizing user selection and power control in wireless networks with fairness constraints.
method Formulated as a Lagrangian dual problem, RRM policies are parameterized by a GNN architecture trained on channel conditions.
result The method achieves superior tradeoff between average and 5th percentile rates, demonstrating fairness.
The flip graph and arc complex of a surface are shown to have finite rigidity.
problem Finite rigidity of flip graph and arc complex for surfaces.
method Embedding the flip graph in the arc complex and leveraging finite rigidity of the flip graph.
result Finite rigidity of the flip graph implies finite rigidity of the arc complex.
New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
DefNet defends GNNs against adversarial attacks by identifying and mitigating vulnerabilities.
problem Vulnerability of GNNs to adversarial attacks.
method Investigates latent vulnerabilities in GNN layers, proposes dual-stage aggregation and bottleneck perceptron, and uses adversarial contrastive learning for training.
result DefNet significantly improves GNN robustness under various adversarial attacks.
We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras wit…
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. This will give an expression of the polynomial, defined by M.Las Vergnas in a combinatorial way using matroids as a spec…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a new dual-tree based variational approach for approximating the transition matrix…