arXiv research

Researchers predict butt rot volume using harvester data and remote sensing.

Study tackles infinitely many-armed bandits with rotting rewards, achieving tight regret bounds.

TURB-Rot provides a large database of turbulent rotating flow snapshots for research.

ROTS improves sentence similarity by incorporating structural information.

Study approximate marked length spectrum rigidity in non-positively curved groups.

New algorithm handles both decaying and non-decaying bandit problems.

Thomas Rot discusses a topology theorem at a math conference.

New algorithm reduces regret in infinitely many-armed bandits with decreasing rewards.

We investigate Legendrian graphs in $(\R^3, ξ_{std})$. We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with $tb=-1$ and $rot=0$ if and only if it does not contain $K_4$ as a mi…

The rotation prediction (Rotation) is a simple pretext-task for self-supervised learning (SSL), where models learn useful representations for target vision tasks by solving pretext-tasks. Although Rotation captures information of object shapes, it hardly captures information of textures. To tackle this problem, we intr…

New R-equivalence classes found for torus knot diagrams.

In stochastic multi-armed bandits, the reward distribution of each arm is assumed to be stationary. This assumption is often violated in practice (e.g., in recommendation systems), where the reward of an arm may change whenever is selected, i.e., rested bandit setting. In this paper, we consider the non-parametric rott…

Develops a novel global pooling framework using optimal transport.

Global existence of Willmore flow with boundary via Li-Yau inequality.

The Multi-Armed Bandits (MAB) framework highlights the tension between acquiring new knowledge (Exploration) and leveraging available knowledge (Exploitation). In the classical MAB problem, a decision maker must choose an arm at each time step, upon which she receives a reward. The decision maker's objective is to maxi…

Graph-Triggered Bandits unify rested and restless bandits with graph-defined arm interactions.

New method tracks shifts in infinite-armed bandits without prior knowledge.

We prove two results on the classification of trivial Legendrian embeddings $g: G \rightarrow (S^3,ξ_{std})$ of planar graphs. First, the oriented Legendrian ribbon $R_g$ and rotation invariant $\text{rot}_g$ are a complete set of invariants. Second, if $G$ is 3-connected or contains $K_4$ as a minor, then the unique t…

In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely determined geometric…

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed …

Let $M_n$ be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-space. We construct in a combinatorial way for each natural number $n>1$ a 1-cocycle $R_n$ which represents a non trivial class in $H^1(M_n; \mathbb{Z} [x_1,x_2,...,x_1^{-1},x_2^{-1},...])$, where the number of variabl…

We advocate an optimization-centric view on and introduce a novel generalization of Bayesian inference. Our inspiration is the representation of Bayes' rule as infinite-dimensional optimization problem (Csiszar, 1975; Donsker and Varadhan; 1975, Zellner; 1988). First, we use it to prove an optimality result of standard…

Sustainable management of groundwater resources under changing climatic conditions require an application of reliable and accurate predictions of groundwater levels. Mechanistic multi-scale, multi-physics simulation models are often too hard to use for this purpose, especially for groundwater managers who do not have a…

Let $(M^n,g,\nabla f)$, $n\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\mathbb{S}^{n-1}(c))$ where $\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of curvature $1/c^2$, with $c\in(0,1)$. We prove that if the convergence to the asympto…

New examples of non-simple knots in Lens spaces show rich botany.

New Legendrian bounds for non-fibered knots in 3-manifolds.

The paper proves $n$-transitivity for equivariant diffeomorphisms of manifolds.

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $Ω$ plus a Riemannian metric $\h$ on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizi…

Let $Ω$ be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair $q=\{α,u\}$ of a function $α$ and a vector field $u$ on $Ω$. A field $q$ is {\it harmonic} if $α, u$ are continuous in $Ω$ and $\nablaα={\rm rot\,}u,\,{\rm div\,}u=0$ holds into $Ω$. The space ${\mathscr Q…

We classify Legendrian unknots in overtwisted contact structures on $S^3$. In particular, we show that up to contact isotopy for every pair $(n,\pm(n-1))$ with $n>0$ there are exactly two oriented non-loose Legendrian unknots in $S^3$ with Thurston-Bennequin invariant $n$ and rotation number $\pm(n-1)$. (Only one overt…

We propose a novel visual context-aware filter generation module which incorporates contextual information present in images into Convolutional Neural Networks (CNNs). In contrast to traditional CNNs, we do not employ the same set of learned convolution filters for all input image instances. Our proposed input-conditio…

We present numerical visualizations of Ricci Flow of surfaces and 3-dimensional manifolds of revolution. Ricci_rot is an educational tool which visualizes surfaces of revolution moving under Ricci flow. That these surfaces tend to remain embedded in R3 is what makes direct visualization possible. The numerical lessons …

We study the effect of surgery on transverse knots in contact 3-manifolds. In particular, we investigate the effect of such surgery on open books, the Heegaard Floer contact invariant, and tightness. The overarching theme of this paper is to show that in many contexts, surgery on transverse knots is more natural than s…

The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability d…