arXiv research

By means of color chord diagrams we establish a necessary and sufficient condition for $O$-topological equivalence of functions with one essentially critical point on oriented surfaces with edge. We also calculate the number of $O$-topologically non-equivalent functions with one essentially critical point on oriented s…

Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a generalisation of the hyperbolic gluing equations, which enables the construction of hy…

We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a constant when the graphs differ by at least one edge; this is essentially the tighte…

This paper generalizes octahedral decomposition to links in thickened surfaces.

Essential triangulations connect via specific moves in 3-manifolds.

We define essential and strongly essential triangulations of 3-manifolds, and give four constructions using different tools (Heegaard splittings, hierarchies of Haken 3-manifolds, Epstein-Penner decompositions, and cut loci of Riemannian manifolds) to obtain triangulations with these properties under various hypotheses…

New graph types help identify complex relationships.

Study Dirac operators on incomplete cusp edge spaces, proving self-adjointness and Fredholm properties.

Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.

In his PhD thesis, Abrams proved that, for a natural number n and a graph G with at least n vertices, the n-strand configuration space of G deformation retracts to a compact subspace, the discretized n-strand configuration space, provided G satisfies two conditions: each path between distinct essential vertices (vertic…

Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.

Suppose M is a cusped finite-volume hyperbolic 3-manifold and T is an ideal triangulation of M with essential edges. We show that any incompressible surface S in M that is not a virtual fiber can be isotoped into spunnormal form in T . The proof is based directly on ideas of W. Thurston.

Counterexamples to a conjecture on ribbon graph genus changes were found and proven.

Motivated by an abstract notion of low-level edge detector filters, we propose a simple method of unsupervised feature construction based on pairwise statistics of features. In the first step, we construct neighborhoods of features by regrouping features that correlate. Then we use these subsets as filters to produce n…

The study analyzes sharpness dynamics in neural networks, revealing mechanisms and conditions.

Traffic forecasting is of great importance to transportation management and public safety, and very challenging due to the complicated spatial-temporal dependency and essential uncertainty brought about by the road network and traffic conditions. Latest studies mainly focus on modeling the spatial dependency by utilizi…

Study restricts causal graphs with expert knowledge.

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove…

Improved DL models robust against adversarial attacks for wireless signal classification.

This article improves communication efficiency in distributed ML over wireless networks.

We study real nonsingular projective cubic fourfolds up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in the middle homology. Moreover, we provide a graph whose vertices represent the equivale…

The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston's spinning construction and a volume rigidity result attributed by Dunfie…

A second part of detailed elementary introduction into Khovanov homologies. This part is devoted to reduced Jones superpolynomials. The story is still about a hypercube of resolutions of a link diagram. Each resolution is a collection of non-intersecting cycles, and one associates a 2-dimensional vector space with each…

We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of gr…

Let M be a compact, connected, orientable, irreducible 3-manifold and T' an incompressible torus boundary component of M such that the pair (M,T') is not cabled. By a result of C. Gordon, if S and T are incompressible punctured tori in M with boundary on T' and boundary slopes at distance d, then d is at most 8, and th…

Let M be a compressionbody containing a graph T (with at least one edge) such that \boundary_+ M is parallel to the union of T and \boundary_- M. We extend methods of Hayashi and Shimokawa to classify bridge surfaces for T. The results of this paper are used in later work to show that if a bridge surface for a graph in…

We define a pseudo-inverse for line graphs using linear integer programming.

New method compresses LSTM networks using MPS tensor trains.

TinyBayes detects crop diseases from images on edge devices with high accuracy and minimal resources.

New findings on hyperbolicity of fine curve graphs and their subgraphs.

A well known question of Gromov asks whether every one-ended hyperbolic group $Γ$ has a surface subgroup. We give a positive answer when $Γ$ is the fundamental group of a graph of free groups with cyclic edge groups. As a result, Gromov's question is reduced (modulo a technical assumption on 2-torsion) to the case when…

The complex of curves $\mathcal{C}(S_g)$ of a closed orientable surface of genus $g \geq 2$ is the simplicial complex having its vertices, $\mathcal{C}^0(S_g)$, are isotopy classes of essential curves in $S_g$. Two vertices co-bound an edge of the $1$-skeleton, $\mathcal{C}^1(S_g)$, if there are disjoint representative…

A graph neural network detects beneficial feature interactions for recommender systems.

Wavelets model complex interactions in spatial transcriptomics.

We study the spectral geometric properties of the scalar Laplace-Beltrami operator associated to the Weil-Petersson metric $g_{\mathrm{WP}}$ on $\mathcal M_γ$, the Riemann moduli space of surfaces of genus $γ> 1$. This space has a singular compactification with respect to $g_{\mathrm{WP}}$, and this metric has crossing…

FIVES generates high-order interactive features efficiently and effectively.

Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of similarity that correspond to how a node (i) sends and (ii) receives edges. Using…

Development of stock networks is an important approach to explore the relationship between different stocks in the era of big-data. Although a number of methods have been designed to construct the stock correlation networks, it is still a challenge to balance the selection of prominent correlations and connectivity of …

Many geometric structures associated to surface groups can be encoded in terms of invariant cross ratios on their circle at infinity; examples include points of Teichmüller space, Hitchin representations and geodesic currents. We add to this picture by studying cubulations of arbitrary Gromov hyperbolic groups $G$. Und…

New algorithms verify and search causal graphs with minimal interventions.

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Rando…

Graph Interplay (GIP) improves GSSL performance by enhancing graph-level communications.

Let $S$ be an orientable surface with negative Euler characteristic. For $k \in \mathbb{N}$, let $\mathcal{C}_{k}(S)$ denote the $\textit{k-curve graph}$, whose vertices are isotopy classes of essential simple closed curves on $S$, and whose edges correspond to pairs of curves that can be realized to intersect at most …

Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of such curves admitting representatives that intersect at most k times. We prove that…

Paper detects anomalous edges in social networks using edge exchangeability.

Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for prediction, optimization, and control of diffusion dynamics. Unfortunately, in most ca…

The emergence of various intelligent mobile applications demands the deployment of powerful deep learning models at resource-constrained mobile devices. The device-edge co-inference framework provides a promising solution by splitting a neural network at a mobile device and an edge computing server. In order to balance…