arXiv research

This paper solves a variation of the isoperimetric problem in higher dimensions.

A new screening test for Lasso improves solution speed.

This paper studies certain embedded spheres in closed affine manifolds. For $n \geq 3$, we investigate the dome bodies in a closed affine $n$-manifold $M$ with its boundary homeomorphic to a sphere under the assumption that a developing map restricted to a component of $\partial\hat{M}$ is an embedding onto a strictly …

Hawksmoor's ceiling and Pantheon dome cofferings are explained using conformal mappings and Mercator's projection.

This paper focusses on "safe" screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed "joint" screening test, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respe…

Topological quantum computation with Fibonacci anyons relies on the possibility of efficiently generating unitary transformations upon pseudoparticles braiding. The crucial fact that such set of braids has a dense image in the unitary operations space is well known; in addition, the Solovay-Kitaev algorithm allows to a…

Sullivan showed that there exists $K_0$ such that if $Ω\subset \hat{\mathbb{C}}$ is a simply connected hyperbolic domain, then there exists a conformally natural $K_0$-quasiconformal map from $Ω$ to the boundary ${\rm Dome}(Ω)$ of the convex hull of its complement which extends to the identity on $\partialΩ$. Explicit …

Paper introduces spherical knot mosaics for knot and link invariants.

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.

The lasso model has been widely used for model selection in data mining, machine learning, and high-dimensional statistical analysis. However, with the ultrahigh-dimensional, large-scale data sets now collected in many real-world applications, it is important to develop algorithms to solve the lasso that efficiently sc…

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…

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…

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…

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.

Let B be a thick spherical building equipped with its natural CAT(1) metric and let M be a proper, convex subset of B. If M is open or if M is a closed ball of radius pi/2, then the maximal subcomplex supported by the complement of M is spherical and non contractible.

We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the co…

Sharp lower bound found for area of vector fields on spherical annuli.

New curvature positivity helps classify spherical spaces and complex projective spaces.

The paper classifies equivariant test configurations for spherical varieties.