arXiv research

Sign equivariant networks improve model expressiveness for spectral geometric learning.

New neural network architectures use signed permutation representations for finite groups, improving performance.

In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here a so-called enhanced Burnside ring $\widehat{B}(G)$ of a finite group $G$…

Study uses instanton Floer theory to obstruct knot unknotting operations.

For a 3-manifold $M$ with $b_1(M)=1$ fibered over $S^1$ and the fiberwise gradient $ξ$ of a fiberwise Morse function on $M$, we introduce the notion of amidakuji-like path (AL-path) on $M$. An AL-path is a piecewise smooth path on $M$ consisting of edges each of which is either a part of a critical locus of $ξ$ or a fl…

Research classifies knots based on sliceness and amphichirality.

Study of $η$ invariants on lens spaces detects distinctions invisible to ordinary $η$.

Study reflection symmetry and APS boundary conditions on a warped cylinder.

The paper classifies circle actions on 6D manifolds with isolated fixed points.

Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.

Study optimal partition problem for Q-curvature equations on Einstein manifolds.

Classifies multigraphs for torus actions on 6D manifolds with isolated fixed points.

New algebraic description connects Fukaya category to bordered Floer homology.

Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $Γ$ of orientation-preserving isometries acts freely, so that the quotient $X=M/Γ$ is compact. We prove a vanishing theorem for a half-kernel of a $Γ$-invariant Dirac operator on a $Γ$-equivariant Clifford module over $M$, twisted by …

Study on signed graphs with random signs, focusing on community detection.

SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.

We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…

Novel GNN for signed and directed networks using magnetic signed Laplacian.

Let G be a Lie supergroup and H a closed subsupergroup. We study the unimodularity of the homogeneous supermanifold G/H, i.e. the existence of G-invariant sections of its Berezinian line bundle. To that end, we express this line bundle as a G-equivariant associated bundle of the principal H-bundle G over G/H. We also s…

Defines signed quasiregular curves and proves growth theorem.

Signed networks contain both positive and negative kinds of interactions like friendship and enmity. The task of node classification in non-signed graphs has proven to be beneficial in many real world applications, yet extensions to signed networks remain largely unexplored. In this paper we introduce the first analysi…

In this short note, we compare the combinatorial sign assignment of Manolescu, Ozsvath, Szabo and Thurston for grid homology of knots and links in 3-sphere with the sign assignment coming from a coherent system of orientations on Whitney disks. Although these constructions produce different signs, a small modification …

PyTorch Geometric Signed Directed fills the gap for GNNs on signed and directed graphs.

Proposes a privacy-preserving sign selection method for distributed systems.

Estimates graph curvature and diameter using Laplacian eigenvalues.

The paper discovers patterns in Maass forms' coefficients related to Fricke signs.

Novel CNN array for sign language recognition using wearable IMUs.

The recognition of sign language is a challenging task with an important role in society to facilitate the communication of deaf persons. We propose a new approach of Spatial-Temporal Graph Convolutional Network to sign language recognition based on the human skeletal movements. The method uses graphs to capture the si…

In this paper we use theory of embedded graphs on oriented and compact $PL$-surfaces to construct minimal realizations of signed Gauss paragraphs. We prove that the genus of the ambient surface of these minimal realizations can be seen as a function of the maximum number of Carter's circles. For the case of signed Gaus…

CSNE embeds signed networks by separating structural and fine-grained information.

Signed seminorms linked to real tropical spaces and matroids.

The paper finds sign-changing solutions for a specific type of elliptic equation.

Unified sign-based compression for federated learning with faster convergence.

Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of normalized standard and signless Laplacians of positive and negative edges. We pro…

Signed-permutation coordinate transport improves model alignment across checkpoints.

New method estimates tensors from noisy data with missing entries.

Signed heights of knotoids are defined and studied.

Develops method for learning signed graphs from smooth signals.

A new method learns node embeddings for signed directed networks by capturing both first-order and high-order topologies.

Study of invariants on manifolds with boundary involving equivariant spectral flow and η-invariants.

It is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describi…

Group-equivariant subsampling layers improve CNNs' equivariance.

Study of equivariant ribbon concordance using Khovanov homology.

We present a method for learning the parameters of a Bayesian network with prior knowledge about the signs of influences between variables. Our method accommodates not just the standard signs, but provides for context-specific signs as well. We show how the various signs translate into order constraints on the network …

Traffic sign recognition is an important component of many advanced driving assistance systems, and it is required for full autonomous driving. Computational performance is usually the bottleneck in using large scale neural networks for this purpose. SqueezeNet is a good candidate for efficient image classification of …

Defines a new homomorphism for strongly invertible knots, proving equivariant algebraic concordance.

Study on blow-up behavior of sign-changing solutions for Yamabe equation.

Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.