The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is known about the tilings by other congruent polygons. In this paper, we classify the simplest case, which is the edge-to-edge tilings of the 2-d…
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48 results for “Edge Classifier”
We introduce new sufficient conditions for intrinsic knotting and linking. A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted. We also classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respe…
The study classifies tilings of the sphere by congruent quadrilaterals.
problem Classifying edge-to-edge tilings of the sphere by congruent quadrilaterals.
method Classification of tilings into three classes based on geometric data and parameters.
result Three classes of tilings are identified: 2-layer earth map tilings, quadrilateral subdivisions of the octahedron, and 3-layer earth map tilings.
Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality of errorfully observed graphs. That is, the existence of an edge between two vert…
Gaussian processes classify graphs using vertex and edge features.
problem Graph classification in machine learning.
method Transform graph features into spectral Euclidean features, apply Hodge decomposition.
result Gaussian processes can classify graphs using vertex and edge features.
Researchers develop a method to interpret GNNs by identifying unnecessary edges in NLP models.
problem Understanding which parts of graphs contribute to NLP model predictions.
method A post-hoc method using differentiable edge masking to identify and drop unnecessary edges.
result Large proportions of edges can be dropped without affecting model performance, providing insights into model predictions.
A new framework reduces data upload for image classification while protecting user privacy.
problem Data upload limitations and privacy concerns in cloud-based image classification.
method Unsupervised autoencoder training at edge devices, followed by latent vector transmission to server for classifier training.
result The framework reduces communications overhead and protects user data privacy.
PL-virtual knotsmath.GT
Piecewise-linear virtual knots are discussed and classified up to edge index six.
Develops new methods to create imperceptible image changes that fool classifiers.
problem Improving the robustness of image classifiers by creating subtle changes undetectable to humans.
method Two methods: Edge-Aware and Color-Aware, designed to reduce detectability of image perturbations.
result Demonstrated that the new methods effectively cause misclassification and are computationally efficient.
Paper proves edge-connectivity equals minimum degree for graphs with non-negative curvature.
problem Edge-connectivity vs. minimum degree in graphs with non-negative curvature.
method Analyzes finite connected graphs with non-negative Lin-Lu-Yau curvature.
result Edge-connectivity equals minimum degree for graphs with non-negative curvature.
A graph is 2-apex if it is planar after the deletion of at most two vertices. Such graphs are not intrinsically knotted, IK. We investigate the converse, does not IK imply 2-apex? We determine the simplest possible counterexample, a graph on nine vertices and 21 edges that is neither IK nor 2-apex. In the process, we s…
LoCEC classifies user relationships in large social networks, addressing sparsity issues.
problem Sparse relationship feature and label data in real social platforms.
method Local Community-based Edge Classification (LoCEC) framework with three-phase processing.
result Effective and efficient classification of user relationships in large-scale networks.
A linkage is a finite graph with lengths assigned to each edge. A planar realization is a map to the plane which preserves edge lengths. It can be thought of as a mechanical device formed from stiff rods and rotating joints. We look at the configuration space of all planar realizations of a linkage (following work of K…
Maximal knotless graphsmath.GT
Maximal knotless graphs have at least 74% of their vertices' edges.
problem Characterizing maximal knotless graphs and understanding their edge constraints.
method Analyzing edge maximality and constructing graphs to meet constraints.
result There exists an infinite family of maximal knotless graphs with fewer edges than previously thought.
TinyBayes detects crop diseases from images on edge devices with high accuracy and minimal resources.
problem Automated disease detection for cocoa crops in resource-constrained settings.
method Combines YOLOv8-Nano for lesion localisation, MobileNetV3-Small for feature extraction, and Jacobi prior for Bayesian classification.
result Achieves 78.7% accuracy on Amini Cocoa Contamination Challenge dataset with 9.5 MB model size and 150 ms inference time.
Active search (AS) on graphs focuses on collecting certain labeled nodes (targets) given global knowledge of the network topology and its edge weights under a query budget. However, in most networks, nodes, topology and edge weights are all initially unknown. We introduce selective harvesting, a variant of AS where the…
Graph attention improves node classification by distinguishing important edges.
problem Node classification in graph-based learning models.
method Theoretical analysis of graph attention networks for node classification.
result Graph attention can perfectly classify nodes in an 'easy' regime but fails in a 'hard' regime.
The study classifies singularities in discrete improper affine spheres.
problem Classifying singularities in discrete improper affine spheres.
method Analysis of discrete improper affine spheres based on asymptotic nets, distinguishing singular edges and vertices.
result First step in classifying singularities of discrete nets.
A new discrete formula connects vertex and edge distributions on graphs.
problem Optimal transport on graphs with mixed vertex and edge distributions.
method Discrete transport equation and Benamou-Brenier formulation.
result Classification of all Wasserstein-1 geodesics on graphs.
Study finds PLI functional connectivity feature superior for depression recognition.
problem Effective detection of depression remains a public health challenge.
method Resting state EEG data collected from MDD and normal controls; various feature types and selection methods evaluated.
result PLI functional connectivity feature superior to linear and nonlinear features; highest classification accuracy 82.31%.
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.
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership information. In particular, we introduce a edge weight distribution matrix to the s…
LAGCN improves GCN performance by identifying and using valuable neighbors.
problem Existing GCN models do not identify valuable neighbors, potentially harming performance.
method LAGCN introduces a label-aware edge classifier to refine the graph and enhance learning performance.
result LAGCN significantly improves node classification performance on benchmark datasets.
We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic knotting of graphs on 8 vertices. For graphs in these families, we verify a conjecture presented in Adams' "The Knot Book": If a vertex is remo…
SGD works well with large learning rates at the edge of stability.
problem Stochasticity at the edge of stability in deep learning.
method Sharp convergence guarantees for SGD with multiclass cross-entropy loss.
result SGD self-stabilizes, ensuring convergence with large learning rates.
We study the geometry of cuspidal singularities in obtained by folding generically a cuspidal edge. In particular we study the geometry of the cuspidal cross-cap , i.e. the cuspidal singularity. We study geometrical invariants associated to and show that they determine it up to order 5.…
Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.
problem Determining the stick number and edge length of knots in a hexagonal lattice.
method Introducing a linear transformation between lattices to prove strict inequalities and classifying knots.
result Only trefoil and figure-eight knots are 11-stick knots in the hexagonal lattice.
We study the geometry of the cuspidal edge in derived from its contact with planes and lines (referred to as flat geometry). The contact of with planes is measured by the singularities of the height functions on . We classify submersions on a model of by diffeomorphisms and recover the cont…
A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, and the 13 graphs obtained from by moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…
RSAC improves lightweight continuous learning efficiency.
problem Excessive training time and memory usage in continuous learning.
method Regularized subspace approximation classifier with feature reduction and regularization.
result RSAC achieves more efficient continuous learning than prior methods.
Gradient descent forces neural network eigenvalues to a specific threshold.
problem Understanding why gradient descent drives eigenvalues to a specific threshold.
method Introduced edge coupling, a functional on consecutive iterate pairs, to explain the trajectory towards the eigenvalue threshold.
result Gradient descent forces the Hessian eigenvalue to the threshold from arbitrary initialization.
In this paper we provide a principled approach to solve a transductive classification problem involving a similar graph (edges tend to connect nodes with same labels) and a dissimilar graph (edges tend to connect nodes with opposing labels). Most of the existing methods, e.g., Information Regularization (IR), Weighted …
Semantic boundary and edge detection aims at simultaneously detecting object edge pixels in images and assigning class labels to them. Systematic training of predictors for this task requires the labeling of edges in images which is a particularly tedious task. We propose a novel strategy for solving this task, when pi…
The study classifies graphs on surfaces with positive curvature properties.
problem Classifying graphs on surfaces with specific curvature properties.
method Using medial graphs and classification techniques.
result Complete classification of graphs on surfaces with positive Forman curvature and corner curvature.
Improved financial network predictability using LLM for edge filtering.
problem Spurious edges in financial networks from textual similarity.
method Two-stage framework: sparse candidate graph + LLM edge classification.
result LLM-based edge filtering improves Sharpe ratio and reduces drawdown.
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
DistShap parallelizes GNN explanation for large graphs.
problem Computational expense in attributing GNN predictions to specific edges or features.
method Distributed Shapley values across multiple GPUs for scalable GNN explanations.
result DistShap outperforms existing methods and scales to models with millions of features.
The paper studies fundamental domains in H^3 and their associated polyhedra.
problem Understanding the relationship between polyhedra and groups associated with fundamental domains in H^3.
method Analyzes torsion-free groups and edge classes of abstract polyhedra, proving results about group properties and edge classes.
result Classifies fundamental domains on the cube with torsion-free groups and provides insights into polyhedra and groups.
Paper proves inequality for capillary hypersurfaces in a wedge.
problem Proving a best version of Heintze-Karcher inequality for capillary hypersurfaces.
method Utilized Heintze-Karcher method and modified parallel hypersurfaces.
result Classified capillary constant mean curvature hypersurfaces hitting the edge in a wedge.
The paper studies connectivity properties of Morse complexes as simplicial complexes grow.
problem Understanding connectivity of Morse complexes as simplicial complexes evolve.
method Bestvina-Brady Morse theory applied to a generalized Morse complex.
result Proves becomes arbitrarily highly connected as grows.
Improved DL models robust against adversarial attacks for wireless signal classification.
problem Adversarial attacks on deep learning-based wireless signal classifiers.
method Knowledge distillation and network pruning followed by adversarial training.
result Proposed models achieve better robustness and higher accuracy than standard 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…
ECGs improve GNNs for non-homophilic data.
problem Improving GNNs for datasets where nodes are not likely to belong to the same class.
method ECGs rewire GNNs' computation graph to connect nodes likely in the same class using weaker classifiers.
result ECGs improve GNN performance on non-homophilic datasets.
Deep learning models are known to be overconfident in their predictions on out of distribution inputs. There have been several pieces of work to address this issue, including a number of approaches for building Bayesian neural networks, as well as closely related work on detection of out of distribution samples. Recent…
Study tests five popular trading signal families and finds four refuted, one inconclusive, and one not refuted.
problem Testing the viability of five popular trading signal families for generating a positive edge.
method Statistical edge testing, economic viability assessment, and finite-bankroll survival under leverage using exposure-matched benchmarks, stationary-bootstrap confidence intervals, and hierarchical Benjamini-Yekutieli control.
result Four out of five signal families are refuted, one is inconclusive, and one is not refuted.
We consider a family of Kähler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated -bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting Kähler structures all have identical Chern classes. We construct Bott di…
Method detects trajectory outliers using Hodge Laplacian embeddings.
problem Detecting outliers in trajectory data on simplicial complexes.
method Flow-embeddings using Hodge 1-Laplacian of simplicial complexes.
result Classifies trajectories based on topological behavior.