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…
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48 results for “edge apex”
New proof for graphs with 21 edges not 2-apex.
problem Identifying graphs with 21 edges that are not 2-apex.
method Combination of triangle-Y and Y-triangle moves on K7, proving minor minimal properties.
result The 20 Heawood family and 7 Petersen family are minor minimal for not 2-apex and not apex properties.
The study examines six variations of apex graphs and their planar properties.
problem Characterizing apex, edge apex, and contraction apex graphs.
method Defined and analyzed six variations of apex graphs, using the Graph Minor Theorem and determining obstruction graphs.
result Found at least 36, 55, and 82 obstruction graphs for apex, edge apex, and contraction apex respectively.
A simpler proof for apex graphs in McCarty and Thomas' conjecture.
problem Proving a conjecture about apex graphs and their linklessly embeddable properties.
method Shorter and simpler proof for the apex case.
result A shorter and simpler proof for the apex case of the conjecture.
A three-dimensional orthoscheme is defined as a tetrahedron whose base is a right-angled triangle and an edge joining the apex and a non-right-angled vertex is perpendicular to the base. A generalization, called complete orthoschemes, of orthoschemes is known in hyperbolic geometry. Roughly speaking, complete orthosche…
We show that the 14 graphs obtained by moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of and mo…
Most Graphs are Knottedmath.GT
Most graphs are knotted as they grow larger.
problem Understanding the prevalence of knotting in random graphs as they increase in size.
method Four models for random graphs were analyzed to determine the probability of intrinsic knotting.
result The probability of a graph being intrinsically knotted approaches 1 as the number of vertices increases.
Constructions stemming from non-separating planar graphs and their Colin de Verdière invariantmath.CO
New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.
problem Understanding linkability and knotability of graph complements.
method Using maximal non-separating planar graphs to construct examples of maximal linkless and knotless graphs, and analyzing their Colin de Verdière invariant.
result The Colin de Verdière invariant of the complement of a maximal non-separating planar graph satisfies μ(cG) ≤ n-4, and equality holds.
Study hyperbolic 2-spheres with cone points, describing spaces for n=3.
problem Characterize the space of hyperbolic 2-spheres with cone points.
method Analyzing the space for and .
result Detailed description of spaces for and examples for .
The paper proves Schauder estimates on cone products and characterizes harmonic functions.
problem Proving Schauder estimates for metric products of cones.
method Characterizing harmonic functions and using local approximations to measure Hölder continuity.
result Interior Schauder estimates for the Laplacian on cone products are proven.
The abstract discusses smoothing and non-smoothing effects using a metric transformation.
problem Analyzing smoothing and non-smoothing effects in metric measure spaces.
method A transformation of metric measure spaces using the length distance induced by heat kernel measures.
result The transformation smooths some Euclidean cones but not the Heisenberg group.
Continuous metrics on ample bundles lie in infinite-dimensional cones.
problem Understanding the structure of positive metrics on ample line bundles.
method Analyzing bounded graded filtrations and embedding into Mabuchi-flat cones.
result Continuous metrics embed isometrically into the space of positive metrics.
RFCN improves cardiac MRI segmentation by leveraging inter-slice spatial correlations.
problem Improving cardiac MRI segmentation accuracy and efficiency.
method Recurrent fully convolutional neural network (RFCN) that learns from full stack of slices.
result RFCN produces state-of-the-art results, improving contour delineation near heart apex.
The Liouville theorem and -estimate for Calabi-Yau cones establish uniqueness and asymptotic behavior of metrics.
problem Establishing uniqueness and asymptotic behavior of metrics on Calabi-Yau cones.
method Developed a Liouville theorem and -estimate for Ricci-flat, conical Kähler manifolds.
result Uniformly bounded Kähler metrics on a ball around the apex are asymptotic to the Ricci-flat cone metric with polynomial decay.
Existence of harmonic maps near projections in hyperbolic spaces for large convex sets.
problem Existence of harmonic maps near projections in hyperbolic spaces.
method Weak quasi-isometry condition, non-collapsing property, harmonic measures.
result Existence of harmonic maps at finite distance from projections of large convex sets in hyperbolic spaces.
3D Consistent & Robust Segmentation of Cardiac Images by Deep Learning with Spatial Propagationcs.CV
Deep learning method for 3D cardiac segmentation with spatial propagation.
problem Cardiac segmentation from MRI stacks with spatial consistency.
method Iterative deep learning with U-net for spatial propagation, training on UK Biobank.
result Comparable or better results than state-of-the-art, enhanced spatial consistency.
Paper detects anomalous edges in social networks using edge exchangeability.
problem Detecting anomalous edges in directed social networks.
method Exploits edge exchangeability and uses conformal prediction theory.
result Proposed anomaly detector has a guaranteed upper bound for false positives.
RL agent learns to place limit orders for trading signals in financial markets.
problem Training an RL agent to execute trading signals in limit order book markets.
method Deep Duelling Double Q-learning with APEX architecture, using synthetic alpha signals.
result RL agent outperforms heuristic trading strategies in inventory management and order placing.
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently…
Optimizes edge coloring in graph bundling for better edge differentiation.
problem Difficulty in identifying origins and destinations of individual edges in strongly bundled graphs.
method Optimizes edge coloring based on pairwise edge strength and origin-destination dissimilarity, solving a nonlinear optimization problem.
result Peacock bundles enhance graph layout comprehensibility with edge differentiation.
Study parallel and dual surfaces of cuspidal edges, defining ridge points and clarifying geometric relations.
problem Understanding the geometric properties of cuspidal edges and their duals.
method Analyzing principal curvature and direction, defining ridge points, and examining geometric relations.
result Clarified relations between singularities of parallel and dual surfaces and cuspidal edges.
The article studies factorization structures in geometry and their applications to cones and polytopes.
problem Understanding and characterizing factorization structures in geometry.
method Comprehensive study of factorization structures, including structure theory, construction of compatible polytopes and cones, and derivation of generalised Gale's evenness condition.
result Established generalised Vandermonde identities and found examples of Delzant and rational Delzant compatible polytopes.
The paper characterizes chordal graphs via edge deletions and finds a local minimum spanning tree algorithm.
problem Characterizing chordal graphs and finding efficient minimum spanning trees.
method Focus on exposed edges, characterize chordal graphs via deletions, and use local properties to modify Kruskal's algorithm.
result A modified Kruskal's algorithm for weighted chordal graphs is local and efficient.
Duality on generalized cuspidal edges preserving singular set images and first fundamental formsmath.DG
Extends duality preserving singular set images and first fundamental forms to generalized cuspidal edges.
problem Preserving singular set images and first fundamental forms on generalized cuspidal edges.
method Extends previous isometric duality to generalized cuspidal edges including cuspidal cross caps and 5/2-cuspidal edges.
result New geometric insights on the duality.
OL4EL optimizes edge learning on resource-constrained servers.
problem Resource constraints on edge servers hinder effective distributed machine learning.
method Online Learning for EL (OL4EL) framework using budget-limited multi-armed bandit model.
result OL4EL significantly improves learning performance while conserving resources.
Paper proposes an edge detection method for robot navigation using low-SNR thermal cameras.
problem Efficient edge detection for robot navigation using low-SNR thermal camera.
method Raw image denoising, Canny edge detection, CSS method, edge ranking, edge linking.
result Enhanced edge detection method effectively detects smooth edges of the surrounding environment.
New GPs model edge functions on complex networks, capturing divergence and curl.
problem Modeling flow data on networks with independent learning of Hodge components.
method Developed Hodge-compositional edge GPs using Hodge decomposition.
result Hodge-compositional edge GPs can represent any edge function and capture flow relevance.
In L^3, cuspidal edges can have bounded mean curvature under specific conditions.
problem Understanding cuspidal edges with bounded mean curvature in Lorentz-Minkowski 3-space.
method Investigated cuspidal edges and generalized cuspidal edges, analyzing their singular points and principal curvatures.
result Cuspidal edges with bounded mean curvature in L^3 occur only when the singular set is a light-like curve.
Positive Ricci curvature achieved by adding edges in a graph.
problem Achieving positive Ricci curvature in graphs.
method Adding edges to a complete graph to increase Ricci curvature.
result Least number of edges needed for positive Ricci curvature.
Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field is well-defined as a smooth vector field of the surface. A cuspidal edge singular point is called generic if the osculating plane of the cuspidal edge (as a regul…
Edge augmentation connects disconnected graphs by elevating eigenvalues.
problem Connecting disconnected subgraphs in graphs with zero eigenvalues.
method Elevating zero eigenvalues of graph's spectrum to connect subgraphs.
result The algorithm consistently connects graph components, achieving >50% inter-community edges.
New framework discovers roles of edges in graphs.
problem Previous work focused on node roles, this tackles edge roles.
method Generalizable framework for learning and extracting edge roles from arbitrary graphs.
result Demonstrates utility of edge roles for network analysis.
Study geometric properties of cuspidal edges with boundary.
problem Differential geometric properties of cuspidal edges with boundary.
method Analysis of differential geometric invariants and their relations.
result Relation between boundary behavior and other invariants.
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…
New maximally linkless graphs found with fewer edges.
problem Finding graphs without any links in 3D space.
method Demonstrated new maximally linkless graphs with improved edge count.
result Found maximally linkless graphs with edges.
Study of cuspidal edges on focal surfaces of regular surfaces.
problem Clarifying the sign of singular curvature at cuspidal edges.
method Investigation using singularities of parallel surfaces.
result Clarification of the sign of singular curvature at cuspidal edges.
RECON reconstructs regulatory networks from time-course data, reducing spurious edges and preserving true regulatory edges.
problem Reconstructing regulatory networks from time-course data with minimal spurious edges and preserving true regulatory relationships.
method RECON uses an integral-based additive nonparametric ODE model with five methodological advances to reconstruct regulatory networks.
result RECON consistently outperforms existing methods, reducing spurious edges and preserving true regulatory edges across various scenarios.
Method certifies edge predictions with cloud-level reliability.
problem Ensuring reliability of edge intelligence models.
method Conformal alignment-based cascading mechanism.
result Certifies conditional coverage with user control over risk level.
Estimates the first non-zero eigenvalue using Ricci curvature on graph edges.
problem Estimating the first non-zero eigenvalue of the Laplacian on graph edges.
method Defining edge distance, studying coarse Ricci curvature, and using Jost-Horak's Laplacian definition.
result Obtained an estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature for a regular graph.
Defending Collaborative Filtering Recommenders via Adversarial Robustness Based Edge Reweightingcs.LG
Defense against user shilling attacks in collaborative filtering using edge reweighting.
problem Vulnerability of collaborative filtering to profile injection attacks.
method Adversarial robustness based edge reweighting to attenuate non-robust edges.
result Effective defense against various types of attacks demonstrated through experiments.
New framework exploits edge features in graph neural networks for improved performance.
problem Insufficient utilization of edge features in current graph neural networks.
method Proposes a new framework with doubly stochastic normalization and multi-dimensional edge feature handling.
result Improves performance on graph node classification and regression tasks.
A hybrid neural network optimizes AI deployment on edge and cloud for energy efficiency.
problem Energy and resource constraints in edge devices for deep learning models.
method Conditionally deep hybrid neural network with quantized layers at edge and full-precision layers at cloud.
result Early classification at the edge reduces energy consumption by 5.5x on CIFAR-10 dataset.
This work surveys attacks and defenses on edge neural networks.
problem Security challenges of edge neural networks due to their compute and memory intensity, data-independence, and privacy risks.
method Taxonomy of attacks and defenses on edge-deployed neural networks.
result New security considerations and approaches are needed for edge DNNs.
CoMGNN models heterogeneous graphs with evolving nodes and edges.
problem Modeling complex, evolving graphs with diverse information.
method Meta graph attention on co-evolving heterogeneous graphs.
result Significant improvement over state-of-the-art methods.
Study relates Gaussian curvature signs to cuspidal edge types and geometric invariants.
problem Understanding the relationship between Gaussian curvature and singularities of Gauss maps of cuspidal edges.
method Analyzes geometric invariants and types of singularities of Gauss maps to define and characterize positivity/negativity of cusps.
result Defines and characterizes positivity/negativity of cusps of Gauss maps by geometric invariants of cuspidal edges, and shows relation between sign of cusps and Gaussian curvature.
This paper proposes a method to learn graph representations by partitioning edges into communities.
problem Graph neural networks ignore how edges are formed, leading to suboptimal representation learning.
method Introduces a generative model to partition edges into community-specific weighted edges, then uses these for GNN-based inference and classification.
result The method learns discriminative representations for both node-level and graph-level classification tasks.
New research finds six bipartite intrinsically knotted graphs with 23 edges.
problem Identifying intrinsically knotted bipartite graphs with 23 edges.
method Analyzing embeddings and graph minors to find minimal intrinsically knotted graphs.
result No minor minimal intrinsically knotted bipartite graph exists with 23 edges.
Study on eta and rho invariants on incomplete edge spaces.
problem Existence and properties of eta and rho invariants on incomplete edge spaces.
method Microlocal analysis of heat kernel asymptotics and Atiyah-Patodi-Singer arguments.
result Derivation of an Atiyah-Patodi-Singer index theorem for incomplete edge spaces.