arXiv research

Proves uniqueness of translators in 3D space.

Study classifies translators for mean curvature flow in 3D.

We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space. Some of the translators resemble well-known minimal surfaces (Scherk's doubly periodic minimal surfaces, helicoids), but others have no…

Finite entropy translating solitons in slabs have quantized entropy and unique structure.

Study long-term behavior of semi-Markov modulated processes using integral functions.

If a Lie algebra structures $\gG$ on a vector space is the sum of a family of mutually compatible Lie algebra structures $\gG_i$, we say that $\gG$ is \emph{simply assembled} from $\gG_s$'s. By repeating this procedure several times one gets a family of Lie algebras \emph{assembled} from $\gG_s$'s. The central result o…

Empirical law predicts accuracy of Google Translate's translation chains.

The authors of (Cho et al., 2014a) have shown that the recently introduced neural network translation systems suffer from a significant drop in translation quality when translating long sentences, unlike existing phrase-based translation systems. In this paper, we propose a way to address this issue by automatically se…

Study on rigidity of translating hypersurfaces not in graphical direction.

The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g > 1 the order of this group is naturally bounded in terms of g due to a Riemann-Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maxima…

Researchers classify and describe $K^α$-translators in Euclidean space.

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

The quality of machine translation is rapidly evolving. Today one can find several machine translation systems on the web that provide reasonable translations, although the systems are not perfect. In some specific domains, the quality may decrease. A recently proposed approach to this domain is neural machine translat…

Study measures gender bias in machine translation using multiple reference points.

Classifies and constructs translators for curvature flows.

This paper uses LLMs and cycle consistency for better machine translation evaluation.

Word translation is a problem in machine translation that seeks to build models that recover word level correspondence between languages. Recent approaches to this problem have shown that word translation models can learned with very small seeding dictionaries, and even without any starting supervision. In this paper w…

Paper finds a non-existence theorem for certain translators in high dimensions.

Constructing translating solitons from Lagrangian Grim Reapers.

Study on singular points of translation surfaces under linearly dependent conditions.

New families of translation surfaces with multiple oblivious points discovered.

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…

This paper classifies grim reapers in a specific product space.

Local Neural Operators enable efficient system-level analysis of complex PDEs.

Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to maximize the translation performance. The models proposed recently for neural ma…

Study invariant $λ$-translators in Lorentz-Minkowski space.

Unique minimal translation surfaces found in Heisenberg group.

Study classifies and characterizes translators in hyperbolic static universe.

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

The quality of neural machine translation can be improved by leveraging additional monolingual resources to create synthetic training data. Source-side monolingual data can be (forward-)translated into the target language for self-training; target-side monolingual data can be back-translated. It has been widely reporte…

Study translators in Generalised Robertson-Walker spacetimes, identifying warping functions and classifying examples.

The paper shows how integrating categorical semantics can enhance unsupervised domain translation.

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

African languages are numerous, complex and low-resourced. The datasets required for machine translation are difficult to discover, and existing research is hard to reproduce. Minimal attention has been given to machine translation for African languages so there is scant research regarding the problems that arise when …

Neural machine translation (NMT) is a recent and effective technique which led to remarkable improvements in comparison of conventional machine translation techniques. Proposed neural machine translation model developed for the Gujarati language contains encoder-decoder with attention mechanism. In India, almost all th…

Study shows only grim reaper cylinder for certain self-translating surfaces.

Study proves conditions for translating solitons to be planar.

We study volume growth, entropy and stability for translating solitons of mean curvature flow. First, we prove that every complete properly immersed translator has at least linear volume growth. Then, by using Huisken's monotonicity formula, we compute the entropy of the grim reaper and the bowl solitons. We also give …

Researchers create annular translators for mean curvature flow.

We introduce and describe the results of a novel shared task on bandit learning for machine translation. The task was organized jointly by Amazon and Heidelberg University for the first time at the Second Conference on Machine Translation (WMT 2017). The goal of the task is to encourage research on learning machine tra…

The paper classifies special surfaces in a 3D space.

Improved understanding of translating solitons using new techniques.

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.

Classifies orbit closures in translation surface strata.

The paper classifies invariant translators for a specific curvature flow.

Recent GAN-based architectures have been able to deliver impressive performance on the general task of image-to-image translation. In particular, it was shown that a wide variety of image translation operators may be learned from two image sets, containing images from two different domains, without establishing an expl…

In this paper we study the second fundamental form of translation surfaces in E3. We give a non-existence result for polynomial translation surfaces in E3 with vanishing second Gaussian curvature KII. We classify those translation surfaces for which KII and H are proportional. Finally we obtain that there are no II-min…

In this paper, we study a new learning paradigm for Neural Machine Translation (NMT). Instead of maximizing the likelihood of the human translation as in previous works, we minimize the distinction between human translation and the translation given by an NMT model. To achieve this goal, inspired by the recent success …