arXiv research

The paper classifies and describes translators in $SL(2,\mathbb{R})$ under specific symmetry conditions.

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

TransCF improves recommendation by modeling user-item relationships with translation vectors.

In this paper, we study Clifford-Wolf translations of Finsler spaces. We first give a characterization of Clifford-Wolf translations of Finsler spaces in terms of Killing vector fields. In particular, we show that there is a natural correspondence between Clifford-Wolf translations and the Killing vector fields of cons…

New families of translating solitons found in hyperbolic space.

The paper calculates gap distributions for translation surfaces, focusing on the double heptagon.

The paper classifies certain types of Lagrangian translators and self-expanders in complex 2-space.

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…

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…

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 …

This is a review with examples concerning the concepts of affine (in particular, constant and linear) vector fields and fundamental vector fields on a manifold. The affine, linear and constant vector fields on a manifold are shown to be in a bijective correspondence with the fundamental vector fields on it of respectiv…

The paper explores singular minimal translation graphs in Euclidean spaces.

We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,R)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocyle-invariant ergodic measures. These measures are supported on closed immersed manifolds with boundary th…

Characterizes ruled translating solitons in Minkowski 3-space.

The paper classifies special surfaces in a 3D space.

We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that McMullen's polytope algebra is a subalgebra of the (partial) convolution algebra …

A $λ$-translating soliton with density vector $\vec{v}$ is a surface in Euclidean space whose mean curvature $H$ satisfies $2H=2λ+\langle N,\vec{v}\rangle$, where $N$ is the Gauss map. We classify all $λ$-translating solitons that are invariant by a one-parameter group of translations and a one-parameter group of rotat…

The paper defines a Chern-Simons invariant for stably trivial vector bundles and uses it to obstruct conformal immersions.

The isotropic 3-space \mathbb{I}^{3} is a real affine 3-space endowed with the metric dx^{2}+dy^{2}. In this paper we describe Weingarten and linear Weingarten affine translation surfaces in \mathbb{I}^{3}. Further we classify the affine translation surfaces in \mathbb{I}^{3} that satisfy certain equations in terms of …

This research tackles automatic paraphrasing without translation.

A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m-dimensional complex vector space which are covariant under the complex special linear group.

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

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

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 spaces of Sp(n)-, Sp(n)U(1)- and Sp(n)Sp(1)- invariant, translation invariant, continuous convex valuations on the quaternionic vector space H^n are studied. Combinatorial dimension formulas involving Young diagrams and Schur polynomials are proved.

ConvCNP models translation equivariance in data.

The paper classifies rotational K^α-translators in Minkowski space.

Automates API mapping across languages with minimal manual effort.

Paper refines Alesker-Bernig-Schuster theorem, proving Hodge-Riemann relations for Euclidean balls.

The space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of Brunn-Minkowski, Aleksandrov-Fenchel…

Golden L surface has unbounded bunching of saddle connections

Paper introduces Laplace-HDC for better binary hyperdimensional computing.

The paper classifies solitons in the Heisenberg space.

A $λ$-translating soliton with density vector $\vec{v}$ is a surface $Σ$ in Euclidean space ${\mathbb R}^3$ whose mean curvature $H$ satisfies $2H=2λ+\langle N,\vec{v}\rangle$, where $N$ is the Gauss map of $Σ$. In this article we study the shape of a compact $λ$-translating soliton in terms of its boundary. If $Γ$ is …

A new model CDT improves cross-domain recommendation by learning translation vectors.

The paper proves instability of translating λ-solitons and provides bounds on their length.

In many regular cases, there exists a (properly defined) limit of iterations of a function in several real variables, and this limit satisfies the functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a vector. This is a special case of a well-known translation equation. In this paper we present a …

We introduce different bases for the vector space of $\mathrm{Sp}(2)\mathrm{Sp}(1)$-invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.

Harmonic basis vector fields on surfaces

In this paper we study solitons invariant with respect to the flow generated by a complete Killing vector field in a ambient Riemannian manifold. A special case occurs when the ambient manifold is the Riemannian product $(\mathbb{R} \times P, {\rm d}t^2+g_0)$ and the Killing field is $X=\partial_t$. Similarly to what h…

Classifies geodesic vectors in low-dimensional Lie algebras.

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…

The paper explores how the Gauss curvature of Riemannian surfaces can be represented as the divergence of a vector field.

The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the complex special linear group is established in a 2-dimensional complex vector space. Every such valuation is given by the sum of a valuation of degree of homogeneity 1 and 3. In dimens…

New model adds persistent memory to self-attention layers for improved performance.

Study infinite superelliptic curves and their Veech groups, providing geometric and algebraic insights.

Proposes a neural network for EMG classification that handles skewness and kurtosis.