arXiv research

This paper classifies curves in genus two handlebodies.

According to the Tits conjecture proved by Crisp and Paris, [CP], the subgroups of the braid group generated by proper powers of the Artin elements are presented by the commutators of generators which are powers of commuting elements. Hence they are naturally presented as right-angled Artin groups. The case of subgroup…

This paper classifies knots with simple curves in genus 2 handlebodies.

A link L is called Brunnian if every proper sublink of L is trivial. Similarly, a bottom tangle T is called Brunnian if every proper subtangle of T is trivial. In this paper, we give a small subalgebra of the n-fold completed tensor power of U_h(sl_2) in which the universal sl_2 invariant of n-component Brunnian bottom…

The study shows that certain cubical presentations lead to aspherical spaces.

We introduce the notion of a bicollapsible 2-complex. This allows us to generalize the hyperbolicity of one-relator groups with torsion to a broader class of groups with presentations whose relators are proper powers. We also prove that many such groups act properly and cocompactly on a CAT(0) cube complex.

In the study of discontinuous groups for non-Riemannian homogeneous spaces, the idea of "continuous analogue" gives a powerful method (T. Kobayashi [Math. Ann. 1989]). For example, a semisimple symmetric space G/H admits a discontinuous group which is not virtually abelian if and only if G/H admits a proper SL(2,R)-act…

Study identifies regions where scoring rules reliably detect forecast errors.

The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the function. In particular, the nonzero level sets of a homogeneous polynomial are proper…

Conductor galloping is the high-amplitude, low-frequency oscillation of overhead power lines due to wind. Such movements may lead to severe damages to transmission lines, and hence pose significant risks to the power system operation. In this paper, we target to design a prediction framework for conductor galloping. Th…

Hotelling's $T^2$-test for the mean of a multivariate normal distribution is one of the triumphs of classical multivariate analysis. It is uniformly most powerful among invariant tests, and admissible, proper Bayes, and locally and asymptotically minimax among all tests. Nonetheless, investigators often prefer non-inva…

New concept of proper-calibeating extends classic calibrated forecasts to proper scoring rules.

Extends biquandle brackets to psyquandles for knot and pseudoknot invariants.

New method for simplifying knots with specific properties.

While recent progress has spawned very powerful machine learning systems, those agents remain extremely specialized and fail to transfer the knowledge they gain to similar yet unseen tasks. In this paper, we study a simple reinforcement learning problem and focus on learning policies that encode the proper invariances …

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family …

The paper explores proper actions and their relation to representation theory, with new quantitative methods.

Classifies $π_1$-injective maps between non-compact surfaces.

In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Us…

We show that immersed minimal surfaces of $\mathbb{R}^{3}$ with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map is injective the whole surface is a wide component. Prior to these results it wa…

In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar Kähler metric on a compact Kähler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates needed, but rather there are necessary modifications adapted to th…

Paper develops proper, lower-bounded losses for weakly supervised classification.

Non-proper surface group action on product of trees found.

Analytic linearization and holomorphic extensions for proper groupoids.

Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.

A study of proper affine vector fields in plane symmetric static space-times by using the rank of the Rieman matrix and holonomy. Studying proper affine vector fields in each case, It is shown that the special class of the above space-times admit proper affine vector fields.

A novel framework quantifies uncertainty using proper scores for various tasks.

First example of open manifold with positive Ricci curvature and non-proper Busemann function.

We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a uniformly distributed random variable) defined on a closed, bounded interval Ω\subset …

First proper learning algorithm for Gaussian halfspaces with matching sample and computational complexity.

Paper analyzes proper losses and their performance in machine learning tasks.

Authors create stable proper biharmonic maps from unit ball to spheres.

Reduces constructing multiplicative connections to simpler tasks.

Proper actions on bornological spaces are characterized with compatible coarse structures.

We prove that the density function of the gradient of a sufficiently smooth function $S : Ω\subset \mathbb{R}^d \rightarrow \mathbb{R}$, obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of $φ=\exp\left(\frac{i…

New method constructs proper affine actions of groups in higher dimensions.

Estimates proper calibration errors and refinement terms in probabilistic predictions.

Embeddings of pairs of disjoint nonparallel primitive simple closed curves in the boundary of a genus two handlebody are classified. Briefly, two disjoint primitives either lie on opposite ends of a product $F \boldsymbol{\times} I$, or they lie on opposite ends of a kind of "twisted" product $F \widetilde{\boldsymbol{…

Proves existence of proper solutions for inverse mean curvature flow.

In this paper we prove that every proper Lie groupoid admits a desingularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits a desingularization to a regular Riemannian proper Lie groupoid, arbitrarily close to the original one in the Gromov-Hausdorff distance betwee…

Study proper actions of Lie groups on symmetric spaces, finding rigidity results and Hurwitz-Radon numbers.

Study on proper learning under relaxed worst-case robust loss for VC classes.

We prove that every bordered Riemann surface admits a complete proper holomorphic immersion into a ball of C^2, and a complete proper holomorphic embedding into a ball of C^3.

First we show that a curvature-adapted proper complex equifocal submanifold is a principal orbit of a Hermann type action under certain condition. Next we show that a proper complex equifocal submanifold is curvature-adapted under certain condition.

In this paper, using the framework of equivariant differential geometry, we study proper $SO(p+1) \times SO(q+1)$-invariant biconservative hypersurfaces into the Euclidean space ${\mathbb R}^n$ ($n=p+q+2$) and proper $SO(p+1)$-invariant biconservative hypersurfaces into the Euclidean space ${\mathbb R}^n$ ($n=p+2$). Mo…

Proper proximality proved for various groups on non-positive curvature spaces.

In [5] I solved the Thom's conjecture that a proper Thom map is triangulable. In this paper I drop the properness condition in the semialgebraic case and, moreover, in the definable case in an o-minimal structure.

In this paper, we study Mabuchi metrics on Fano manifolds. We prove that Mabuchi metrics exist if the modified Ding functional is proper modulo a reductive subgroup of its automorphism group. On the other hand, the inverse that Mabuchi metrics implies the properness is obtained by using Darvas-Rubinstein's properness p…