arXiv research

The paper proves uniqueness of evolving graphs by mean curvature flow under specific conditions.

Estimates prove existence of curvature flow in curved spaces.

In this paper, following J. Franks' work on Lyapunov graphs of nonsingular Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on $S^1 \times S^2$. More precisely, we determine necessary and sufficient conditions on an abstract Lyapunov graph to be associated with a nonsingular Smale flow on $S^1 …

In this note we study a large class of mean curvature type flows of graphs in product manifold $N\times R$ where N is a closed Riemann- ian manifold. Their speeds are the mean curvature of graphs plus a prescribed function. We establish long time existence and uniformly convergence of those flows with a barrier conditi…

Paper proves stability of flow in cotangent bundle for special Lagrangian submanifolds.

Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…

MoFlow generates chemically valid molecular graphs from latent representations.

We consider mean curvature flow of an initial surface that is the graph of a function over some domain of definition in $R^n$. If the graph is not complete then we impose a constant Dirichlet boundary condition at the boundary of the surface. We establish longtime-existence of the flow and investigate the projection of…

The paper solves curvature problems on graphs using a special flow.

DECAF optimizes molecular graphs for ensemble properties, improving drug design accuracy.

Graph Neural Networks model 3D granular flow simulations.

The Ollivier Ricci flow with prescribed curvature on infinite graphs.

Let $M$ be a complete Riemannian manifold which either is compact or has a pole, and let $\varphi$ be a positive smooth function on $M$. In the warped product $M\times_\varphi\mathbb R$, we study the flow by the mean curvature of a locally Lipschitz continuous graph on $M$ and prove that the flow exists for all time an…

GC-Flow uses graph flows for better clustering than traditional GCNs.

The study connects geodesic flows on Riemann surfaces to random walks on their dual graphs.

Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.

Analyzes Willmore flow for graphs with boundary data, proving existence and convergence.

In this paper we study nonparametric mean curvature type flows in $M\times\mathbb{R}$ which are represented as graphs $(x,u(x,t))$ over a domain in a Riemannian manifold $M$ with prescribed contact angle. The speed of $u$ is the mean curvature speed minus an admissible function $ψ(x,u,Du)$. Long time existence and unif…

Graphs with nonnegative Bakry-Émery curvature have volume doubling and Poincaré inequalities.

BGNNs model particle-boundary interactions efficiently.

We consider a fully nonlinear parabolic equation with nonlinear Neumann type boundary condition, and show that the longtime existence and convergence of the flow. Finally we apply this study to the boundary value problem for minimal Lagrangian graphs.

MLPF uses graph neural networks to improve particle-flow reconstruction in high-pileup conditions.

We introduce vine computational graphs for efficient ML integration of vine copulas.

Let f:Σ_1 --> Σ_2 be a map between compact Riemannian manifolds of constant curvature. This article considers the evolution of the graph of f in the product of Σ_1 and Σ_2 by the mean curvature flow. Under suitable conditions on the curvature of Σ_1 and Σ_2 and the differential of the initial map, we show that the flow…

We consider the mean curvature flow of entire Lagrangian graphs with Lipschitz continuous initial data. Assuming only a certain bound on the Lipschitz norm of an initial entire Lagrangian graph in $\R^{2n}$, we show that the parabolic equation \eqref{PMA} for the Lagrangian potential has a longtime solution which is sm…

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …

iGNN tackles inverse graph prediction using invertible neural networks.

We recall the construction of the Kontsevich graph orientation morphism $γ\mapsto {\rm O\vec{r}}(γ)$ which maps cocycles $γ$ in the non-oriented graph complex to infinitesimal symmetries $\dot{\mathcal{P}} = {\rm O\vec{r}}(γ)(\mathcal{P})$ of Poisson bi-vectors on affine manifolds. We reveal in particular why there alw…

In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a functional adapted from the area functional. We construct barriers to show that f…

GANF uses normalizing flows to detect anomalies in multiple time series.

Existence and uniqueness theorem for Ricci flow on weighted graphs proved.

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area-decreasing map between unit spheres (of possibly different dimensions) is homotopic to a constant…

Constructs graph manifolds with many Anosov flows.

New method shows pseudo-Anosov flows on graph manifolds can be simplified.

New curvature defined via graph resistances leads to Ricci flow.

The paper explores heat flow and constants on graphs, proving properties and proposing new concepts.

New method learns discrete graph diffusion via free-energy gradient flows.

Graph neural network using Beltrami flow for feature and topology evolution.

A novel spatio-temporal graph neural network with a learnable Tweedie head improves vessel traffic flow prediction in sparse maritime data.

Study curve shortening flows on specific surfaces, proving properties and existence.

Study of mean curvature flows on graphs in warped product manifolds, focusing on behavior at infinity.

New Ricci flow method for directed graphs with balancing factor.

Local existence and uniqueness of Bakry-Émery Ricci flow solutions on finite graphs.

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly reduced memory footprint, allowing them to scale to larger graphs. In the unsupervis…

The paper introduces a new type of Ricci flow on graphs to study their curvature.

Graph Ricci flow reveals hidden hierarchies in stock market correlations.

Study on planar graphs in Poincare model of hyperbolic geometry.

Study shows how to preserve Lagrangian condition in mean curvature flow on Kim-McCann metrics.