arXiv research

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

In this note, we embed the set of all Fricke characters of a free group F -- the set of all characters of representations of F into SL(2,C) -- as an irreducible affine variety V in complex affine space of dimension 2^n-1. Using the Horowitz generating set as the indeterminates, we show that the ideal I of all polynomia…

The first eigenvalue of the Laplacian on a unique Hurwitz surface has a sevenfold multiplicity and specific numerical values.

The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action on R^3 by polyno…

Let $Σ$ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce regular globally hyperbolic anti-de Sitter structures on $Σ\times \mathbb{R}$ and provide two parameterisations of their deformation space: as an enhanced product of two copies of the Fricke space of $Σ$ and as the b…

This is a mathematical commentary on Teichm{ü}ller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl{ä}chen'' (Determination of extremal quasiconformal maps of closed oriented Riemann surfaces). This paper is among the last (and may be the last one) that Teich…

The rigidity of marked length spectrum for closed hyperbolic surfaces due to Fricke-Klein [7] has been the motivation of many different rigidity results, specially for manifolds of negative curvature. From the works of Vigneras [18], Sunada [17] and many other authors this result is far from being true for the unmarked…

Given a closed binding curve $γ$ of a surface $Σ$, any equivalence class of marked complete hyperbolic structure can be decomposed into polygons(possibly with a puncture) with sides being hyperbolic geodesic segments. When $Σ$ is a one-holed torus and $γ= A^3 B^2$, we show that any equivalence class of marked complete …

Deformation spaces Hom($π$,G)/G of representations of the fundamental group $π$ of a surface $Σ$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_Σ$, preserving a Poisson structure. When $G$ is compact, the actions are ergodic. In contrast if $G$ is noncompact semisimple, the associated deformat…

Let pi be a free group of rank 2. Its outer automorphism group Out(pi) acts on the space of equivalence classes of representations in Hom(pi, SL(2,C)). Let SLm(2,R) denote ths subset of GL(2,R) consisting of matrices of determinant -1 and let ISL(2,R) denote the subgroup (SL(2,R) union i SLm(2,R)) of SL(2,C). The repre…

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.

Sign equivariant networks improve model expressiveness for spectral geometric learning.

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.

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…

Method predicts which high-dimensional correlation signs will change in the future.

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.

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…

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 …

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

We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant $p$-gerbes with $p\geq-1$, which give rise to sign choices and are related by coboundary maps. We prove that the sign choice homomorphisms stabilise with the dimension…

New nodal domain theorems for symmetric matrices via signed graphs.

For a spanning tree T of a connected graph G and for a labelling φ: E(T) \rightarrow {+, -}, φis called an alternating sign on a spanning tree T of a graph G if for any cotree edge e \in E(G)-E(T), the unique path in T joining both end vertices of e has alternating signs. In the present note, we prove that any graph ha…

Unified model for signed networks separates balance and anomaly effects.

Regularized spectral methods improve clustering in signed graphs, especially for sparse data.

Improved upper bound for mass partitioning problem using Gray codes.

Study on compact Kähler surfaces for sign-changing curvatures.

We introduce a property of mutation loops, called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropical $\mathcal{X}$-transformation. A sign-stable mutation loop has a numerical invariant which we call the cluster stretch factor, in analogy with that of a pseudo-Anosov mapping clas…

Voice-controlled personal and home assistants (such as the Amazon Echo and Apple Siri) are becoming increasingly popular for a variety of applications. However, the benefits of these technologies are not readily accessible to Deaf or Hard-ofHearing (DHH) users. The objective of this study is to develop and evaluate a s…