Related papers: Graphical Translators for Mean Curvature Flow
We show that there are five types of planar curves such that arrangements of its translates are combinatorially equivalent to an arrangement of lines. These curves can be used to define norms giving constructions with many unit distances…
In this work, we propose a flow-adapter architecture for unsupervised NMT. It leverages normalizing flows to explicitly model the distributions of sentence-level latent representations, which are subsequently used in conjunction with the…
This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. First, we introduce a class of generalized curvatures, and prove the existence and uniqueness for the…
In the half-space model of the hyperbolic three space with the hyperbolic metric, this same space can be seen as the Lie group, hence, a translation surface is a surface that is given by the product of two curves $\alpha$ and $\beta$ in…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…
We study the graphs generated when the formula for linking Markov triples is applied to general triples of integers. We find there are a finite number of equivalence classes of graphs, each with particular properties.
We study some basic problems of translating solitons: the volume growth, generalized maximum principle, Gauss maps and certain functions related to the Gauss maps, finally we carry out point-wise estimates and integral estimates for the…
We derive local $C^{2}$ estimates for complete non-compact translating solitons of the Gauss curvature flow in $\mathbb{R}^3$ which are graphs over a convex domain $\Omega$. This is closely is related to deriving local $C^{1,1}$ estimates…
We describe several families of permutation polynomials obtained using functions with linear translators.
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
We prove that any complete immersed globally orientable uniformly 2-convex translating soliton $\Sigma \subset \mathbb{R}^{n+1}$ for the mean curvature flow is locally strictly convex. It follows that a uniformly 2-convex entire graphical…
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only…
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…
Draft of textbook chapter on neural machine translation. a comprehensive treatment of the topic, ranging from introduction to neural networks, computation graphs, description of the currently dominant attentional sequence-to-sequence model,…
This paper shows the existence of convex translating surfaces under the flow by the $\alpha$-th power of Gauss curvature for the sub-affine-critical regime $ 0 < \alpha < 1/4$. The key aspect of our study is that our ansatz at infinity is…
The representation learning on textual graph is to generate low-dimensional embeddings for the nodes based on the individual textual features and the neighbourhood information. Recent breakthroughs on pretrained language models and graph…
The notion of translation (shift) is straightforward in classical signal processing, however, it is challenging on an irregular graph structure. In this work, we present an approach to characterize the translation operator in various signal…
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…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.