arXiv research

The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.

A Heegaard splitting which admits a unique pair of disjoint compression disks on distinct sides is said to be keen weakly reducible. This paper provides an construction of keen weakly reducible Heegaard splittings of arbitrary genus except 2. Furthermore, critical Heegaard splittings may yield if we change some conditi…

We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological index of F is two if F is topologically minimal.

This paper studies properties of weak reducing pairs in critical Heegaard splittings.

New proof confirms 4-manifolds with weakly reducible genus-three trisections are standard.

Hierarchical text classification has many real-world applications. However, labeling a large number of documents is costly. In practice, we can use semi-supervised learning or weakly supervised learning (e.g., dataless classification) to reduce the labeling cost. In this paper, we propose a path cost-sensitive learning…

New examples of knots with special bridge positions found.

This paper studies the question of whether minimal genus Heegaard splittings of exterior spaces of knots which are connected sums are weakly reducible or not. Furthermore it is shown that the Heegaard splittings of the knots used by Morimoto to show that tunnel number can be sub-additive are all strongly irreducible. T…

Solves weakly supervised regression using low-rank approximations and manifold regularization.

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M and DVW(F) the subset of the disk complex D(F) consisting of simplices having at least one vertex from V and at least one vertex from W. In this article, we describe the shape of DVW(F) and prove t…

In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider Cartan space with the m-th root metric. We prove that every m-th root Cartan space of isotropic Landsberg curvature, or isotropic mean Landsberg curvature, or isotropic mean Berwald curvature reduces to a Landsberg, weakly …

Algorithm transforms weakly negative plumbing trees to negative definite ones.

This paper considers a semi-supervised learning framework for weakly labeled polyphonic sound event detection problems for the DCASE 2019 challenge's task4 by combining both the tri-training and adversarial learning. The goal of the task4 is to detect onsets and offsets of multiple sound events in a single audio clip. …

Improves label propagation for weakly supervised learning.

Paper tackles weakly supervised learning from similarity-confidence data.

In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal $β$-change of an m-th…

Develops a new SPP algorithm with variance reduction for weakly convex optimization.

In this paper, we characterize locally dually flat and Antonelli $m$-th root Finsler metrics. Then, we show that every $m$-th root Finsler metric of isotropic mean Berwald curvature reduces to a weakly Berwald metric.

Let $M$ be an orientable, irreducible $3$-manifold admitting a weakly reducible genus three Heegaard splitting as a minimal genus Heegaard splitting. In this article, we prove that if $[f]$, $[g]\in Mod(M)$ give the same correspondence between two isotopy classes of generalized Heegaard splittings consisting of two Hee…

In the literature, there are two different notions of pseudosymmetric manifolds, one by Chaki [7] and other by Deszcz [16], and there are many papers related to these notions. The object of the present paper is to deduce necessary and sufficient conditions for a Chaki pseudosymmetric [7] (resp. pseudo Ricci symmetric […

We introduce the notion of weak reduciblity for Dupin submanifolds with arbitrary codimension. We give a complete characterization of all weakly reducible Dupin submanifolds, as a consequence of a general result on a broader class of Euclidean submanifolds. As a main application, we derive an explicit recursive procedu…

Dark blockchain venues increase miners' profits but raise users' execution risk.

RAN model recognizes multiple activities from unlabeled sensor data.

Study Anosov representations of reducible suspensions of hyperbolic groups.

UREs lead to overfitting in complex models, especially in complementary label learning.

Weakly Einstein Kähler surfaces are characterized and classified.

The study examines weakly Einstein Lie groups and proves non-existence for certain types.

Classifies weakly Einstein submanifolds in space forms satisfying specific equalities.

The study explores weakly $p$-Kähler hyperbolic manifolds.

Optimizes learning policies in MDPs with weakly communicating structure.

Study 4D steady gradient Ricci solitons reducing to 3D manifolds.

JoCoR improves deep learning with noisy labels by reducing network diversity.

In this paper it is shown that manifolds admitting minimal genus weakly reducible but irreducible Heegaard splittings contain an essential surface. This is an extension of a well known theorem of Casson-Gordon to manifolds with non-empty boundary. The situation for non-minimal genus Heegaard splittings is also investig…

Study weakly weighted Einstein-Finsler metrics, showing specific curvature properties and characterizing them.

New proof of Haken's Lemma and Scharlemann's theorem using thin position.

Minimal displacement set in weakly systolic complexes is systolic and embeds isometrically.

Study on extended weakly symmetric spaces, classifying and providing an example.

There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit…

Classifies weakly Einstein hypersurfaces in spaces of constant curvature.

We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of s-representations.

The paper examines Randers metrics with isotropic scalar curvature properties.

New examples of weakly Einstein conformal products are constructed.

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n+1)-dimensional Sasakian manifold admits a weakly Einstein metric then its scalar curvature $s$ satisfies $-6\leqslant s \leqslant 6$ for $n=1$ and $-2n(2n+1)\frac{4n^2-4n+3}{4n^2-4n-1}\leqslant s \leqslant …

The holonomy algebra $\g$ of an indecomposable Lorentzian (n+2)-dimensional manifold $M$ is a weakly-irreducible subalgebra of the Lorentzian algebra $\so_{1,n+1}$. L. Berard Bergery and A. Ikemakhen divided weakly-irreducible not irreducible subalgebras into 4 types and associated with each such subalgebra $\g$ a suba…

Characterizes weakly linked pairs of complete graphs in 3D space.

The object of the present note is to discuss about the defining condition of weakly cyclic Ricci symmetric manifolds and weakly cyclic $Z$-symmetric manifolds \cite{DMS15} and the existence of such notion by proper examples.

Classifies weakly Einstein curvature tensors in 4D Euclidean space.