arXiv research

Derives TAP approximation for Bayesian linear regression.

Bayesian framework for sphere regression using Gaussian fields.

SAE improves VAE's latent space precision in high dimensions.

New method uses spherical harmonics to simplify learning single-index models.

Proposes a new latent variable model for hyperspherical latent spaces.

New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.

EM algorithm achieves optimal sample complexity for well-separated Gaussian mixtures.

Study of naked singularities in Einstein vacuum equations using new self-similarity.

Paper introduces spherical knot mosaics for knot and link invariants.

Noise in SGD affects overparameterized models, favoring sparse solutions.

Study geodesics on spherical polyhedra, estimating their number.

The abstract proves spherical surface decompositions with conical singularities.

For the n-dimensional spherical pedal curve $ped_{γ,P}$ with respect to an n-dimensional spherical unit speed curve $γ$ and a given point $P \in S^n$, we define the spherical orthotomic curve of $γ$ relative to the point $P$, and classify singularities of spherical orthotomic curves.

Study spherical curves with curvature dependent on distance to a great circle.

Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.

New findings show fundamental group is not audible in spherical space forms.

Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.

The reductivity of a spherical curve represents how reduced the spherical curve is. It is unknown if there exists a spherical curve whose reductivity is four. In this paper we give an unavoidable set for spherical curves with reductivity four by considering 4-gons.

The paper improves inequalities for nearly spherical sets using quermassintegrals.

The reductivity of a spherical curve is the minimal number of a local transformation called an inverse-half-twisted splice required to obtain a reducible spherical curve from the spherical curve. It is unknown if there exists a spherical curve whose reductivity is four. In this paper, an unavoidable set of configuratio…

Gradient descent fails to learn simple neural networks efficiently.

We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by four or less inverse-half-twisted splices, i.e., the reductivity, which represents how reduced a spherical curve is, is four or less. We also discuss unavoidable sets of tangles for spherical curves.

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area…

Extends diffusion models to non-Euclidean spaces with geometric priors.

Study on spherical CR manifolds with non-trivial Chern classes.

PGF kernels analyze spherical data using generalized RBF kernels.

The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.

Classifies involutions on spherical 3-manifolds.

The paper classifies spherically symmetric Finsler metrics as Berwaldian or Riemannian.

Paper develops invariants for spherical curves using chord diagrams.

In this paper we consider the spherical slant helices in $R^3$. More- over, we show how could be obtained to a spherical slant helix and we give some spherical slant helix examples in Euclidean 3-space.

The paper characterizes spherically symmetric metrics with scalar curvature.

The study proves spherical polygon analogs of curve theorems, finding bounds on intersections and inflections.

New formula for spherical polygon area via prequantization.

Euler explored spherical geometry using trigonometric formulae and solid geometry methods.

A spherical polyhedron surface is a triangulated surface obtained by isometric gluing of spherical triangles. For instance, the boundary of a generic convex polytope in the 3-sphere is a spherical polyhedron surface. This paper investigates these surfaces from the point of view of inner angles. A rigidity result is obt…

The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general existence theory. Our main contribution is proving that there exist …

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or trees, the heterogeneity of the relational data typically encountered in practic…

Recently we initiated the study of spherical T-duality for spacetimes that are principal SU(2)-bundles. In this paper, we extend spherical T-duality to spacetimes that are oriented non-principal SU(2)-bundles. There are several interesting new examples in this case and a new phenomenon appearing in the non-principal ca…

Kähler-Ricci flow on spherical Fano manifolds converges to a soliton.

Spherical Plateau problem studies minimal surfaces in quotients of spheres.

The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.

In earlier papers, we introduced spherical T-duality, which relates pairs of the form $(P,H)$ consisting of an oriented $S^3$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$ called the 7-flux. Intuitively, the spherical T-dual is another such pair $(\hat P, \hat H)$ and spherical T-duality exchanges the 7-flux with …

We introduce spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$. Intuitively spherical T-duality exchanges $H$ with the second Chern class $c_2(P)$. Unless $dim(M)\leq 4$, not all pairs admit spherical T-duals and the spheric…

DELIMIT is a framework extension for deep learning in diffusion imaging, which extends the basic framework PyTorch towards spherical signals. Based on several novel layers, deep learning can be applied to spherical diffusion imaging data in a very convenient way. First, two spherical harmonic interpolation layers are a…

Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.

Researchers find highest volumes for isospectral spherical orbifolds and space forms.