arXiv research

G2Gs transforms target molecules into reactants without templates, improving accuracy.

Study on finiteness property of right-angled Artin groups actions on extension graphs.

Uniqueness of circle packings on certain translation surfaces is proven.

The aim of this work is studying translating graphs by mean curvature flow in $\Real^3$. We prove non-existence of complete translating graphs over bounded domains in $\Real^2$. Furthermore, we show that there are only three types of complete translating graphs in $\Real^3$; entire graphs, graphs between two vertical p…

Inspired by the tremendous success of deep generative models on generating continuous data like image and audio, in the most recent year, few deep graph generative models have been proposed to generate discrete data such as graphs. They are typically unconditioned generative models which has no control on modes of the …

Study on stable translation lengths of surface homeomorphisms and their approximations.

This paper tackles graph translation challenges by predicting both node and edge attributes simultaneously.

We view molecular optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be optimized in different ways, there are multiple viable translations for each input graph…

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

To every half-translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the underlying half-translation surfaces. We also investigate the automorphism group of the …

The paper explores new translating solitons and their relation to $Δ$-wings.

The paper proves a stability result for translating space-like graphs in Lorentz manifolds.

We show that an Anosov map has a geodesic axis on the curve graph of a torus. The direct corollary of our result is the stable translation length of an Anosov map on the curve graph is always a positive integer. As the proof is constructive, we also provide an algorithm to calculate the exact translation length for any…

New curves defined by curvature powers studied for variational properties.

In this paper we provide a full classification of complete translating graphs in $\mathbf{R}^3$. We also construct two $(n-1)$-parameter families of new examples of translating graphs in $\mathbf{R}^{n+1}$.

The study examines translation lengths of pseudo-Anosov maps on curve graphs.

New findings on translation lengths in Teichmüller and curve graphs for pseudo-Anosovs.

New bound for group action length without diameter restriction.

Circle packings on translation surfaces are consistent across different surfaces.

In this paper, we compute the first and second variation formulas for the F-functional of translating solitons and study the Hamiltonian L-stability of Lagrangian translating solitons. We prove that any Lagrangian translating soliton is Hamiltonian L-stable.

In this work, we study graphs in $\M^n\times\Real$ that are evolving by the mean curvature flow over a bounded domain on $\M^n$, with prescribed contact angle in the boundary. We prove that solutions converge to translating surfaces in $\M^n\times\Real$. Also, for a Riemannian manifold $\M^2$ with negative Gaussian cur…

The process of translation is ambiguous, in that there are typically many valid trans- lations for a given sentence. This gives rise to significant variation in parallel cor- pora, however, most current models of machine translation do not account for this variation, instead treating the prob- lem as a deterministic pr…

The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$. In this paper we describe a full classification of complete translating graphs i…

Automorphisms and subdivisions of Helly graphs are studied, leading to explicit models and rational translation lengths.

We prove the existence of horizontal Jenkins-Serrin graphs that are translating solitons of the mean curvature flow in Riemannian product manifolds $M\times\mathbb{R}$. Moreover, we give examples of these graphs in the cases of $\mathbb{R}^3$ and $\mathbb{H}^2\times\mathbb{R}$.

The study classifies and investigates translators invariant under hyperpolar actions on symmetric spaces.

In this paper, we show that the minimal asymptotic translation length of the Torelli group $\mathcal{I}_g$ of the surface $S_g$ of genus $g$ on the curve graph asymptotically behaves like $1/g$, contrary to the mapping class group $Mod(S_g)$, which behaves like $1/g^2$. We also show that the minimal asymptotic translat…

The paper proves stability of certain graph types in Euclidean space with specific densities.

The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the Reidemeister moves for links into the language of intersection graphs of chord diagrams. I…

The study proves stability of various graphical translators in mean curvature flow.

Our research extends the Bilingual Evaluation Understudy (BLEU) evaluation technique for statistical machine translation to make it more adjustable and robust. We intend to adapt it to resemble human evaluation more. We perform experiments to evaluate the performance of our technique against the primary existing evalua…

The paper classifies shapes of translating solitons for a specific flow.

In this article we prove two non-existence results for translating solitons of the mean curvature flow (translators for short) in $\mathbb{R}^{m+1}$. We also obtain an upper bound to the maximum height that a compact embedded translator in $\mathbb{R}^{3}$ can achieve. On the other hand, we study graphical perturbation…

The paper classifies shapes of translating solitons from isoparametric graphs.

Graphs from van der Corput sequence embed into Chamanara surface.

The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on graph-to-graph translation methods for molecular optimization. In particular, we realize …

Graph-to-Tree Neural Networks improve structured input-output translation in tasks like semantic parsing and math word problems.

NTKs explain GNNs' alignment for graph prediction.

Study on stability of 3D sessile drops, identifying degenerate kernel.

Proposes local coordinate frames for improving model performance in complex dynamical systems.

The study explores normal generators for mapping class groups and their properties.

In this note we discuss graphs over a domain $Ω\subset N^2$ in the product manifold $N^2\times \mathbb{R}$. Here $N^2$ is a complete Riemannian surface and $Ω$ has peice-wise smooth boundary. Let $γ\subset\partialΩ$ be a smooth connected arc and $Σ$ be a complete graph in $N^2\times \mathbb{R}$ over $Ω$. We show that i…

A new memory-efficient sign language translation model reduces weight usage.

Paraphrasing exemplifies the ability to abstract semantic content from surface forms. Recent work on automatic paraphrasing is dominated by methods leveraging Machine Translation (MT) as an intermediate step. This contrasts with humans, who can paraphrase without being bilingual. This work proposes to learn paraphrasin…

We consider the problem of making machine translation more robust to character-level variation at the source side, such as typos. Existing methods achieve greater coverage by applying subword models such as byte-pair encoding (BPE) and character-level encoders, but these methods are highly sensitive to spelling mistake…

BasisVAE combines VAE and clustering for tabular data analysis.

The paper proves properties of surfaces with finite curvature in 3D space.

The aim of this paper is to study variational properties for $f$-minimal Lagrangian submanifolds in Kähler manifolds with real holomorphy potentials. Examples of submanifolds of this kind incuding soliton solutions for Lagrangian mean curvature flow (LMCF). We derive second variation formula for $f$-minimal Lagrangians…