arXiv research

Study finds central points of double heptagon surface are not connection points.

Study confirms non-injective monodromy for even genus 4 translation surfaces.

Federated CycleGAN enables privacy-preserving image translation without central data.

Characterizes flat affine symplectic Lie groups and their properties.

The study of random walks on hyperbolic spaces and Teichmüller spaces, proving central limit theorems and geodesic tracking.

Study of flows on circle bundles over translation surfaces, showing decay of correlations.

This handbook translates lead time analysis into R code.

Mime algorithm improves federated learning by adapting centralized methods.

Multimodal sentiment analysis is a core research area that studies speaker sentiment expressed from the language, visual, and acoustic modalities. The central challenge in multimodal learning involves inferring joint representations that can process and relate information from these modalities. However, existing work l…

In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the a…

Study on connection points on double regular polygons, providing coordinates and proving non-connection points.

The paper studies complex curves with translation structures from differential equations.

NAST generalizes scattering transform for non-stationary time series analysis.

We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in $\mathfrak{so}(\mathbb{R}^q)$, translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, in…

Multimodal machine learning is a core research area spanning the language, visual and acoustic modalities. The central challenge in multimodal learning involves learning representations that can process and relate information from multiple modalities. In this paper, we propose two methods for unsupervised learning of j…

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponenti…

We implement a differential-geometric approach to normal forms for contracting measurable cocycles to $\mbox{Diff}^q({\bf R}^n, {\bf 0})$, $q \geq 2$. We obtain resonance polynomial normal forms for the contracting cocycle and its centralizer, via $C^q$ changes of coordinates. These are interpreted as nonstationary inv…

The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.

Random square-tiled surfaces have normal genus distribution and cover all integer vectors.

ATD measures language distance using neural models, recovering linguistic groupings.

The question of whether a representation of Artin's pure braid group is faithful is translated to certain properties of the Lie algebra arising from the descending central series of the pure braid group, and thus the Vassiliev invariants of pure braids via work of T. Kohno \cite{kohno1,kohno2}. The main result is a Lie…

Existence proved for $q$-Bass martingales with specific marginals.

The theme of this paper is that algebraic complexity implies dynamical complexity for pseudo-Anosov homeomorphisms of a closed surface S_g of genus g. Penner proved that the logarithm of the minimal dilatation for a pseudo-Anosov homeomorphism of S_g tends to zero at the rate 1/g. We consider here the smallest dilatati…

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…

Develops a simulation-based method to translate expert knowledge into prior distributions for Bayesian models.

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide …

New bounds on generalization error for distributed learning using rate-distortion theory.

Paper proposes a method to learn word translations bidirectionally.

Study on rigidity of translating hypersurfaces not in graphical direction.

Forward translation improves neural machine translation for sentences originally in source language.

Let $S=Γ\backslash \mathbb{H}$ be a hyperbolic surface of finite topological type, such that the Fuchsian group $Γ\le \operatorname{PSL}_2(\mathbb{R})$ is non-elementary, and consider any generating set $\mathfrak S$ of $Γ$. When sampling by an $n$-step random walk in $π_1(S) \cong Γ$ with each step given by an element…

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…

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

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

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…

Neural machine translation models trained for 5 South African languages.

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.

Neural machine translation used to convert CUDA to OpenCL.

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

We discuss in this article a property of action of groups by isometries called "well displacing". An action is said to be well displacing, if the displacement function is equivalent to the the displacement function for the action on the Cayley graph. We relate this property with the fact that orbit maps are quasi-isome…

Constructing translating solitons from Lagrangian Grim Reapers.

Study classifies translators for mean curvature flow in 3D.

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

Proves uniqueness of translators in 3D space.

An NMT system for Indic languages outperforms Google Translate.