Develops neural network for directed hypergraphs for node classification.
problem Irregular data structure, particularly directed graphs.
method Directed hypergraph neural network and semi-supervised learning method.
result Novel directed hypergraph neural network achieves highest accuracies on node classification tasks.
Develops PageRank for directed hypergraphs using metabolic network.
problem Lack of directed hypergraph datasets for PageRank algorithm.
method Developed PageRank algorithm for directed hypergraphs and applied it to metabolic network.
result Successfully applied novel PageRank algorithm to metabolic network.
LayerNorm transformers have dead directions that can be read from their parameters alone.
problem Locating dead directions in LayerNorm transformers
method Using the inverse-scale direction of LayerNorm affine parameters
result Predicted dead direction matches measured bottom singular direction
Paper classifies surfaces with a special direction in Minkowski 3-space.
problem Characterizing surfaces with a canonical principal direction.
method Characterization and classification of surfaces in Minkowski 3-space.
result All surfaces with a canonical principal direction are classified.
The paper defines curvature dimension inequalities on directed graphs and evaluates them.
problem Defining curvature dimension inequalities on directed graphs.
method Defining CD(m, K) on finite directed graphs.
result Evaluates m and K on finite directed graphs.
Introduces directed diagrammatic reducibility with group and topological implications.
problem Diagrammatic reducibility in relative presentations.
method Adapting classical tools for diagrammatic reducibility to directed diagrammatic reducibility.
result Strong group theoretic and topological consequences of directed diagrammatic reducibility.
New method clusters data points by finding optimal directions.
problem Subspace clustering problem, especially in noisy and close subspaces.
method Optimal direction search via convex program, alternating direction method of multipliers.
result Significantly outperforms existing methods, especially in noisy scenarios.
Unsupervised method discovers interpretable directions in GAN latent space.
problem Discovering interpretable directions in GAN latent space without supervision.
method Model-agnostic procedure to identify directions corresponding to semantic manipulations.
result Findings include directions for background removal and competitive saliency detection performance.
New discrete Ricci curvature for directed networks developed.
problem Directed networks require a new curvature measure.
method Extended Forman-Ricci curvature for directed networks, incorporating vertex and edge weights, and edge direction.
result New curvature measure captures higher-order correlations in directed networks.
The paper studies kernel smoothing and mean shift for directional data, deriving convergence rates and mode estimation.
problem Statistical and computational problems of kernel smoothing for directional data.
method Generalization of mean shift to directional data, derivation of convergence rates, and investigation of mode estimation.
result Statistical convergence rates of directional KDE and its derivatives, ascending property of directional mean shift, and mode estimation.
Research preserves coarse property C and related dimensions through direct products.
problem Preserving properties in coarse geometry through direct products.
method Demonstrates preservation of coarse property C and related dimensions through finite coarse direct products.
result Coarse property C and related dimensions are preserved by direct products.
DimeNet uses directional message passing to improve molecular predictions.
problem Lack of directional information in graph neural networks for molecules.
method Directional message passing, rotationally equivariant embeddings, spherical functions.
result DimeNet outperforms previous GNNs by 76% on MD17 and 31% on QM9.
Efficient algorithm learns direct causes and effects from data.
problem Discovering direct causes and effects from data in a large space.
method ELCS algorithm using N-structures and Markov Blanket discovery.
result ELCS achieves better accuracy and efficiency than state-of-the-art methods.
DiMMSB models directed mixed membership networks, identifying distinct community structures.
problem Modeling directed mixed membership networks with distinct community structures.
method Directed Mixed Membership Stochastic Blockmodel (DiMMSB) with DiSP algorithm.
result DiSP algorithm is asymptotically consistent and outperforms competitors.
PyTorch Geometric Signed Directed fills the gap for GNNs on signed and directed graphs.
problem Lack of unified software packages for GNNs on signed and directed networks.
method Developed a software package with GNN models, synthetic and real-world data, and evaluation metrics.
result Demonstrates the effectiveness of the implemented methods through experiments.
This paper classifies singularities of tangent surfaces to directed curves.
problem Classifying singularities of tangent surfaces to directed curves.
method Local diffeomorphism classification of generic directed curves.
result Swallowtails and open swallowtails appear generically for tangent surface singularities.
In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively framed knot complements and study the direct limit. We also study the morphism sp…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraph…
DEDACT breaks down feature importance into direct and associative components.
problem Lack of clear distinction between direct and associative feature importance.
method DEDACT framework to decompose direct and associative importance measures.
result Provides insight into sources of prediction-relevant information and feature pathways.
In this study, we define a new type of direction curves in the Euclidean 3-space such as osculating-direction curve. We give the characterizations for these curves. Moreover, we obtain the relationships between osculating direction curves and some special curves such as helix, slant helix or rectifying curves.
FastMap-D embeds directed graphs using potential fields.
problem Embedding directed graphs in Euclidean space.
method Generalization of FastMap to handle directed graphs using a potential field and machine learning.
result FastMap-D outperforms other approaches in embedding directed graphs.
Harmonic analysis on directed graphs for signal modeling and semi-supervised learning.
problem Signal analysis on directed graphs.
method Introduced a Fourier-type basis using eigenvectors of the random walk operator, developed wavelet transforms for multi-scale analysis.
result Efficiency of the proposed framework for semi-supervised learning and signal modeling on directed graphs.
New toolkit for directed distances improves flexibility of OT problems.
problem Optimal transport problems with constraints.
method Directed distances between quantile functions.
result Flexibility in solving OT problems enhanced.
This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anc…
Study of Betti numbers in prodsimplicial complexes for directed graphs, focusing on DNA recombination.
problem Analyzing Betti numbers in directed graphs for DNA recombination.
method Custom prodsimplicial complexes for acyclic directed graphs, investigating Betti numbers.
result Investigated Betti numbers and cycles in prodsimplicial complexes for DNA recombination.
Classifies surfaces with a special direction in 4D space.
problem Classifying surfaces with a canonical principal direction.
method Complete classification of surfaces in Euclidean 4-space.
result Obtained complete classification of CPD surfaces.
Study on rigidity of translating hypersurfaces not in graphical direction.
problem Rigidity of translating hypersurfaces not in graphical direction.
method Proved rigidity results for complete graphical translating hypersurfaces under specific conditions.
result Entire graphical translating surfaces are flat under certain conditions.
Spectral clustering for directed graphs using likelihood estimation.
problem Clustering directed graphs with edge directions.
method Maximum likelihood estimation on stochastic block models.
result Significant performance gains over existing methods.
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.
Novel GNN for signed and directed networks using magnetic signed Laplacian.
problem Efficiently modeling signed and directed networks for tasks like clustering and link prediction.
method Introduced a magnetic signed Laplacian for directed signed graphs, used it to construct a spectral GNN.
result Demonstrated effective performance on tasks involving signed and directional information.
Improved spectral-based GCN for directed graphs.
problem Cannot directly work on directed graphs.
method Redefined Laplacians to improve propagation model.
result Outperforms state-of-the-art methods on directed graph datasets.
Study directed completion of spacetimes, focusing on Schwarzschild spacetime.
problem Characterizing directed completions of spacetimes.
method Directed completion of Lorentzian pre-length spaces, focusing on Schwarzschild spacetime.
result Directed completion of Schwarzschild spacetime coincides with future causal completion.
New method identifies valid IVs for bi-directional MR with invalid instruments.
problem Estimating causal effects from observational data with invalid instruments and unmeasured confounding.
method Theoretical investigation and cluster fusion-like method to discover valid IV sets.
result Theoretical demonstration and experimental validation of the method's effectiveness.
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field. This is the first generative model of its kind for directed graphs. We introduce…
A new GAN method ensures unbiased updates towards the steepest descent direction.
problem GANs update generator parameters in non-optimal directions.
method Introduces a theoretical framework and divergence approximating Wasserstein distance, ensuring unbiased steepest descent updates.
result Sets a new state-of-the-art on language generation tasks.
Proposes a copula-based model for multi-view clustering with directional dependency.
problem Challenges in integrating multi-source datasets with directional dependency.
method Copula-based multi-view clustering model accounting for directional dependence.
result Ignoring directional dependence negatively impacts clustering performance.
Directed graphs can be intrinsically knotted and 4-linked.
problem Intrinsic linking and knotting in directed graphs.
method Construction of examples and operations (consistent edge contraction, H-cyclic subcontraction).
result Directed graphs can have consistently oriented knotted cycles and intrinsically 3- and 4-linked structures.
In Carnot groups, directional pliability allows curve extensions and approximations.
problem Existence of curve extensions and approximations in Carnot groups.
method Directional pliability in subsets of directions guarantees Whitney-type extensions and Lusin approximations.
result Every horizontal curve in the Engel group intersects a C1 curve in a set of positive measure. Study of curves and surfaces from single-direction projections.
problem Obtaining complete shape information from a single view.
method Theoretical study of differential geometric information from multiple orthogonal projections.
result Formulae for recovering certain information on curves or surfaces from their projections.
The study examines principal directions and curvatures of Lagrangian submanifolds.
problem Understanding the geometry of Lagrangian submanifolds.
method Recalling and analyzing the extrinsic principal tangential and normal directions, and their corresponding curvatures for Lagrangian submanifolds in complex Euclidean spaces.
result Established natural relationships between distinguished tangential and normal directions and their curvatures for Lagrangian submanifolds.
In this note we give a construction of a smooth Riemannian metric on R^n which is standard Euclidean outside a compact set K and such that it has N = n(n + 1)=2 invisible directions, meaning that all geodesics lines passing through the set K in these directions remain the same straight lines on exit. For example in the…
Study geodesic trees and exceptional directions in FPP on hyperbolic groups.
problem Understanding the geometry and uniqueness of geodesics in FPP on hyperbolic groups.
method Analyzing random geodesic trees and exceptional directions in the context of FPP on hyperbolic groups.
result The set of exceptional directions has strictly smaller Hausdorff dimension than the boundary, and hence has measure zero.
Study projective and direct limits of Banach structures with connections to G-structures.
problem Understanding connections between Banach structures and G-structures. method Endow projective and direct limits with Fréchet or convenient structures and study connections.
result Illustrated examples demonstrate the study of projective and direct limits.
Improves community detection in directed networks with theoretical guarantees.
problem Degree heterogeneity affects community detection in directed networks.
method Introduced D-SCORE algorithm and established theoretical guarantees for Directed-DCBM.
result Established theoretical guarantees and provided improvements for D-SCORE.
Study relaxes identification assumptions for natural direct effects in non-randomized settings.
problem Identifying causal direct effects under unmeasured confounding.
method Developed relaxed conditions for identifying natural direct effects in non-randomized settings.
result Identified natural direct effect under unmeasured confounding conditions.
The paper defines and analyzes IC using high-dimensional directional statistics.
problem Defining and analyzing the Information Coefficient (IC) in high-dimensional settings.
method High-dimensional directional statistics, closed-form expressions, optimization, simulation, empirical analysis.
result Explicit results of the projected normal distribution and IC's nature.
New graph AE and VAE model predicts directed links better than existing methods.
problem Link prediction in directed graphs, especially for unobserved edges.
method Gravity-inspired decoder scheme for directed graphs.
result Outperforms standard graph AE and VAE on three real-world directed link prediction tasks.
Paper defines a new dimension to measure self-directed learning complexity.
problem Understanding self-directed learning complexity in online learning theory.
method Developed a dimension SDdim to characterize self-directed learning mistake-bound. result Calculated SDdim for various concept classes and demonstrated learnability gaps.