arXiv research

We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.

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

GROOVE learns representations for weakly paired multimodal data.

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

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 study pairs of Engel structures on four-manifolds whose intersection has constant rank one and which define the same even contact structure, but induce different orientations on it. We establish a correspondence between such pairs of Engel structures and a class of weakly hyperbolic flows. This correspondence is ana…

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

We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost e…

Unified approach for multicalibration in weakly supervised learning.

For a holomorphic one-form $\mathbfξ$ on a weakly 1-complete manifold $X$ with certain properties, we discussed the connectivity of the pair $(\hat{X}, F^{-1}(z))$, where $π: \hat{X} \to X$ is a covering map and $dF=π^*\mathbfξ$. We also discussed the criteria about when such a manifold $X$ admits a proper holomorphic …

New examples of knots with special bridge positions found.

Paper tackles weakly supervised learning from similarity-confidence data.

Neural network models that are not conditioned on class identities were shown to facilitate knowledge transfer between classes and to be well-suited for one-shot learning tasks. Following this motivation, we further explore and establish such models and present a novel neural network architecture for the task of weakly…

Model learns image-word associations from captions using contrastive learning.

The paper examines Yang-Mills-Higgs pairs on vector bundles and proves stability and energy identity.

Combination theorem for geodesic coarsely convex group pairs.

The paper examines boundedness of diffeomorphism groups of manifold pairs, focusing on the circle case.

Recently, researches related to unsupervised disentanglement learning with deep generative models have gained substantial popularity. However, without introducing supervision, there is no guarantee that the factors of interest can be successfully recovered. Motivated by a real-world problem, we propose a setting where …

A computationally simple genome-wide association study (GWAS) algorithm for estimating the main and epistatic effects of markers or single nucleotide polymorphisms (SNPs) is proposed. It is based on the intuitive assumption that changes of alleles corresponding to important SNPs in a pair of individuals lead to large d…

A new method uses preference relations to reconcile contradictory trading signals from multiple securities.

We improve our previous results on indefinite Kasparov modules, which provide a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. In particular, we can weaken the assumptions that are imposed on indefinite Kasparov modules. Using a new theorem by Lesch an…

Weak supervision enables learning causal representations from unstructured data.

We prove that for a weakly exact magnetic system on a closed connected Riemannian manifold, almost all energy levels contain a closed orbit. More precisely, we prove the following stronger statements. Let $(M,g)$ denote a closed connected Riemannian manifold and $σ$ a weakly exact 2-form. Let $φ_{t}$ denote the magneti…

Gopal Prasad and A. S. Rapinchuk defined a notion of weakly commensurable lattices in a semisimple group, and gave a classification of weakly commensurable Zariski dense subgroups. A motivation was to classify pairs of locally symmetric spaces isospectral with respect to the Laplacian on functions. For this, in higher …

Knowledge Matters: Importance of Prior Information for Optimization [7], by Gulcehre et. al., sought to establish the limits of current black-box, deep learning techniques by posing problems which are difficult to learn without engineering knowledge into the model or training procedure. In our work, we completely solve…

Hashing has been widely adopted for large-scale data retrieval in many domains, due to its low storage cost and high retrieval speed. Existing cross-modal hashing methods optimistically assume that the correspondence between training samples across modalities are readily available. This assumption is unrealistic in pra…

Learning disentangled representations that correspond to factors of variation in real-world data is critical to interpretable and human-controllable machine learning. Recently, concerns about the viability of learning disentangled representations in a purely unsupervised manner has spurred a shift toward the incorporat…

A Coxeter $n$-orbifold is an $n$-dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order $m$, whose neighborhood is locally modeled on ${\mathbb R}^n$ modulo the dihedral group of order $2m$ generated by two reflections. For $n \geq 3$, we study…

The paper shows how to transform certain 3-manifold Heegaard splittings into simpler forms.

Recent results using inverse scattering techniques interpret every solution $φ(x,y)$ of the sine-Gordon equation as a non-linear superposition of solutions along the axes $x=0$ and $y=0$. Here we provide a geometric method of integration, as well as a geometric interpretation. Specifically, every weakly regular surface…

Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which o…

Paper studies Minkowskian product of Finsler manifolds and their connections.

We construct a weakly complete flat surface in hyperbolic 3-space having a pair of hyperbolic Gauss maps both of whose images are contained in an arbitrarily given open disc in the ideal boundary of H^3. This construction is accomplished as an application of the minimal surface theory. This looks an interesting phenome…

Weakly Einstein Kähler surfaces are characterized and classified.

Let L be a link in the 3-sphere that is in thin position but not in bridge position and let P be a thin level sphere. We generalize a result of Wu by giving a bound on the number of disjoint irreducible compressing disks that P can have, including identifying thin spheres with unique compressing disks. We also give con…

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…

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.

Let $M$ be a smooth manifold and let $\F$ be a codimension one, $C^\infty$ foliation on $M$, with isolated singularities of Morse type. The study and classification of pairs $(M,\F)$ is a challenging (and difficult) problem. In this setting, a classical result due to Reeb \cite{Reeb} states that a manifold admitting a …

The Bellman error is a poor proxy for value function accuracy, even with all state-action pairs.

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

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.