arXiv research

New families of translation surfaces with multiple oblivious points discovered.

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

The paper proves Morse estimates for translated points on unit tangent bundles.

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

A point q in a contact manifold is called a translated point for a contactomorphism φ, with respect to some fixed contact form, if φ(q) and q belong to the same Reeb orbit and the contact form is preserved at q. The problem of existence of translated points is related to the chord conjecture and to the problem of leafw…

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

Random translation surfaces converge to a Poisson plane as genus grows.

We show that all GL(2,R) equivariant point markings over orbit closures of translation surfaces arise from branched covering constructions and periodic points, completely classify such point markings over strata of quadratic differentials, and give applications to the finite blocking problem.

The paper proves the exact number of singular points in the intersection of convex shapes.

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

A point q in a contact manifold is called a translated point for a contactomorphism φ, with respect to some fixed contact form, if φ(q) and q belong to the same Reeb orbit and the contact form is preserved at q. In this article we discuss a version of the Arnold conjecture for translated points of contactomorphisms and…

Constructing translating solitons from Lagrangian Grim Reapers.

We show that the minimum of asymptotic translation lengths of all point-pushing pseudo-Anosov maps on any one punctured Riemann surface is one.

Classifies periodic points on regular and double n-gon surfaces.

Proves better rigidity theorems for special solitons.

Study of polynomial strata using braid groups and translation surfaces.

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

Study precise rates of horizontal gap shrinkage on generic translation surfaces.

Study shows periodic points of Prym eigenforms in specific genera.

We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varyi…

Formula estimates pseudo-Anosov maps' fixed points, linking to surface properties.

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 …

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 squared norm of the second fundamental form. Those estimates give rigidity theorems…

Let $Γ$ be a finitely generated group and $G$ be a noncompact semisimple connected real Lie group with finite center. We consider the space $\mathcal X$ of conjugacy classes of reductive representations of $Γ$ into $G$. We define the {\it translation vector} of an element $g$ in $G$, with values in a Weyl chamber, as a…

A translating soliton is a hypersurface $M$ in $\mathbb{R}^{n+1}$ such that the family $M_t= M- t \,\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at that point $\mathbf{H}=\mathbf{e}_{n+1}^{\perp}.$ In this paper we obtain a cha…

A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the sam distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous if for any two point $x_1, x_2\in M$ there is a Clifford-Wolf translation $ρ$ such that $ρ(x_1)=x_2$. In this paper, we study Clifford-Wolf transl…

Study calculates slope gaps on polygon surfaces, finding non-unimodal distributions.

The paper classifies surfaces in the Heisenberg space invariant under specific isometries.

A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the same distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous if for any two points $x_1, x_2\in M$ there is a Clifford-Wolf translation $ρ$ such that $ρ(x_1)=x_2$. In this paper, we give a complete classifi…

In the half-space model of hyperbolic space, that is, $\r^3_{+}=\{(x,y,z)\in\r^3;z>0\}$ with the hyperbolic metric, a translation surface is a surface that writes as $z=f(x)+g(y)$ or $y=f(x)+g(z)$, where $f$ and $g$ are smooth functions. We prove that the only minimal translation surfaces (zero mean curvature in all po…

We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of immersions: continuous maps between subsets of translation surfaces that respect the b…

The paper classifies vertices in planar polygons formed by convex domains.

We present a recurrent encoder-decoder deep neural network architecture that directly translates speech in one language into text in another. The model does not explicitly transcribe the speech into text in the source language, nor does it require supervision from the ground truth source language transcription during t…

We show that on any translation surface, if a regular point is contained in a simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in the unit circle. Moreover, the set of points that are not contained in any simple closed geodesic is finite. We also constr…

SE(3)-Transformers maintain equivariance for 3D data under rotations and translations.

A translation structure on a surface is an atlas of charts to the plane so that the transition functions are translations. We allow our surfaces to be non-compact and infinite genus. We endow the space of all pointed surfaces equipped with a translation structure with a topology, which we call the immersive topology be…

Book explores infinite translation surfaces, challenging traditional geometry.

We show that the Bowl soliton in $\mathbb{R}^3$ is the unique translating solutions of the mean curvature flow which has the family of shrinking cylinders as an asymptotic shrinker at $-\infty$. As an application, we show that for a generic mean curvature flow, all (non-static) translating limit flows are the bowl soli…

Given that South African education is in crisis, strategies for improvement and sustainability of high-quality, up-to-date education must be explored. In the migration of education online, inclusion of machine translation for low-resourced local languages becomes necessary. This paper aims to spur the use of current ne…

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…

We characterize subgroups of the mapping class group that stabilize a Teichmueller disk in terms of ellipses and strips that are immersed in the associated translation surface. In particular, we show that the space of immersed ellipses/strips that meet at least three cone points is naturally a (non-manifold) 2-dimensio…

We generalize the notion of Zermelo navigation to arbitrary pseudo-Finsler metrics possibly defined in conic subsets. The translation of a pseudo-Finsler metric $F$ is a new pseudo-Finsler metric whose indicatrix is the translation of the indicatrix of $F$ by a vector field $W$ at each point, where $W$ is an arbitrary …

Although over 100 languages are supported by strong off-the-shelf machine translation systems, only a subset of them possess large annotated corpora for named entity recognition. Motivated by this fact, we leverage machine translation to improve annotation-projection approaches to cross-lingual named entity recognition…

In this paper, we study Clifford-Wolf translations of homogeneous Randers metrics on spheres. It turns out that we can present a complete description of all the Clifford-Wolf translations of all the homogeneous Randers metrics on spheres. The most important point of this paper is that a new phenomena surfaces. Namely, …

Researchers compute gap distributions for saddle connection directions on specific translation surfaces.

We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. This is done by const…

An isometry of a Finsler space is called Clifford-Wolf translation (CW-translation) if it moves all points the same distance. A Finsler space $(M, F)$ is called Clifford-Wolf homogeneous (CW-homogeneous) if for any $x, y\in M$ there is a CW-translation $σ$ such that $σ(x)=y$. We prove that if $F$ is a homogeneous Finsl…

In this paper we investigate the systolic landscape of translation surfaces for fixed genus and fixed angles of their cone points. We furthermore study how the systoles of a translation surface relate to the systoles of its graph of saddle connections. This allows us to develop an algorithm to compute the systolic rati…