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…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “Spherical Framework”
Spherical Knot Mosaicsmath.GT
Paper introduces spherical knot mosaics for knot and link invariants.
problem Representing knots on a sphere with tiles.
method Tiling a 2-sphere with 11 knot mosaic tiles to define new invariants.
result New knot invariants derived from spherical mosaic tiling.
Paper develops invariants for spherical curves using chord diagrams.
problem Developing invariants for spherical curves under local moves.
method Using based chord diagrams and local moves from Reidemeister moves.
result Invariants include both classical and new spherical curve invariants.
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
We classify hyperbolic monopoles with continuous symmetries and construct new examples.
problem Classifying and constructing hyperbolic monopoles with continuous symmetries.
method Developed a Structure Theorem and used representation theory to simplify the problem.
result Found constraints on structure groups and constructed novel spherically symmetric hyperbolic monopoles.
This paper connects geometric diagrams to spherical T-duality.
problem Establishing equivalence between geometric and string-theory frameworks.
method Introducing -diagrams and proving their equivalence to spherical T-dual pairs.
result Concrete geometric realization of spherical T-duality.
Rigidity theorem for spherical sectors in Riemannian manifolds.
problem Rigidity of spherical sectors in Riemannian manifolds under overdetermined conditions.
method Analyzing solutions to the inhomogeneous Helmholtz equation with constant Dirichlet and Neumann boundary conditions.
result Spherical sectors are the only solutions under given conditions.
This paper uses a geometric approach to understand how normalization layers affect neural network optimization.
problem Understanding the effect of normalization layers on optimization in neural networks.
method Introduces a spherical framework to study optimization dynamics of neural networks with normalization layers from a geometric perspective.
result Derives the first effective learning rate expression of Adam and shows that SGD with NLs is equivalent to a constrained variant of Adam.
The paper classifies spherically symmetric sprays and their curvature properties.
problem Understanding spherically symmetric sprays and their curvature.
method Established a canonical form and derived classification for projectively flat sprays.
result Derived explicit forms for sprays with isotropic and zero curvature.
Bayesian framework for sphere regression using Gaussian fields.
problem Nonparametric regression on the sphere with Gaussian priors.
method Isotropic Gaussian field priors, harmonic structure, exact posterior distributions, optimal spectral truncation, posterior contraction rates.
result Sharp posterior contraction rates for Gaussian priors with polynomially decaying angular power spectra.
Paper explores neural network approximations on sphere domains.
problem Approximating functionals on sphere domains using neural networks.
method Encoder-decoder framework with spherical harmonics for infinite-dimensional domain.
result Approximation rates of neural networks with different encoder structures.
Study investigates minimal surfaces in spherical caps, extending previous findings.
problem Characterizing minimal surfaces with free boundaries and capillary conditions in spherical caps.
method Extending previous half-space intersection properties to warped products and capillary minimal surfaces in high codimension.
result Established a dual operation relating free boundary and capillary minimal surfaces.
New symmetries found in Riemann-Cartan geometries.
problem Investigating symmetries in geometries with curvature and torsion.
method Mathematical tools to determine symmetries and subclasses of geometries.
result Determined all static and stationary spherically symmetric Riemann-Cartan geometries and subclasses with specific symmetries.
A new method using spherical harmonics approximates the Sliced-Wasserstein distance.
problem Approximating the Sliced-Wasserstein distance between probability measures.
method Spherical Harmonics Control Variates (SHCV) method for Monte Carlo approximation of the SW distance.
result SHCV method provides an improved rate of convergence compared to Monte Carlo for general measures.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
Geometrically, spherical 3-manifolds emerge from flat SU(2)-bundles over hyperbolic surfaces.
problem Realizing spherical 3-manifolds from flat SU(2)-bundles over hyperbolic surfaces.
method Using Gromov-Hausdorff convergence and systole maximization over moduli spaces.
result Homogeneous spherical 3-manifolds can be realized as limits of metric spaces of flat SU(2)-bundles.
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
Enhances Gaussian processes with spherical features for better scalability and flexibility.
problem Lack of representation learning in Gaussian processes compared to deep neural networks.
method Introduces spherical inter-domain features to improve GP approximation and scalability.
result The method alleviates limitations and improves scalability compared to alternative strategies.
Study geodesics on spherical polyhedra, estimating their number.
problem Counting simple closed geodesics on spherical polyhedra.
method Examined regular spherical octahedra, cubes, and tetrahedra.
result Estimated the number of simple closed geodesics on spherical polyhedra.
New method uses scalar-based models to approximate spherical tensors efficiently.
problem Efficiently approximating spherical tensors with equivariant functions.
method Expressing equivariant functions as the product of a scalar function and a small tensor basis.
result Approximations are fast, simple to implement, and accurate in practical settings.
The abstract proves spherical surface decompositions with conical singularities.
problem Decomposing surfaces with spherical metrics and conical singularities.
method Geometric triangulations and irreducible components of standard shapes.
result Spherical polygons, including half-spherical concave polygons, can be arbitrarily complicated.
For the n-dimensional spherical pedal curve with respect to an n-dimensional spherical unit speed curve and a given point , we define the spherical orthotomic curve of relative to the point , and classify singularities of spherical orthotomic curves.
Study spherical curves with curvature dependent on distance to a great circle.
problem Understanding spherical curves with curvature dependent on distance to a great circle.
method Introducing spherical angular momentum, characterizing known curves, finding new families, and obtaining arc length parametrizations.
result New families of spherical curves with intrinsic equations in elementary or Jacobi elliptic functions.
Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.
problem Understanding eigenvalues and gaps in spherical triangles.
method Explicit computation of Dirichlet eigenvalues and eigenfunctions for spherical lunes and triangles.
result Fundamental gap of spherical triangles increases as the angle of the lune decreases.
New findings show fundamental group is not audible in spherical space forms.
problem Isospectral spherical space forms with non-cyclic fundamental groups.
method Revisited and found new examples of spherical space forms.
result Fundamental group is not audible among spherical space forms.
Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.
problem Existence and uniqueness of spherical helicoidal surfaces in 3-sphere.
method Continuous function of distance to axis, spherical angular momentum of spherical curves.
result Existence and uniqueness theorem for spherical helicoidal surfaces in 3-sphere.
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.
problem Improving inequalities for nearly spherical sets.
method Establishing quantitative Alexandrov-Fenchel inequalities for quermassintegrals.
result Lower bounds on the -isoperimetric deficit found using spherical deviation and asymmetry.
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.
problem Investigating compatibility conditions on spherically symmetric Finsler metrics.
method Using the inverse problem of calculus of variations, the paper focuses on Landsberg and Berwald types.
result All Landsberg spherically symmetric manifolds in higher dimensions are either Riemannian or have specific geodesic spray formulas.
New spherical Milnor spaces for diffeological groups with geometric and topological properties.
problem Understanding higher topological structures in diffeological spaces.
method Spherical Milnor construction based on quadratic normalization.
result Provides a natural setting for studying principal bundles with -twists and higher cohomology.
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.
problem Understanding Chern classes in spherical CR manifolds.
method Construction and proof of constraints on Chern classes.
result Topological obstruction to spherical CR structures on contact manifolds.
FHDMs achieve optimal convergence in spherically supported data.
problem Statistical convergence properties of FHDMs for spherical data.
method FHDMs leverage random generation time and Doob's h-transform to optimize convergence rate.
result Achieve minimax optimal convergence rate in total variation for spherically supported Sobolev smooth data.
PGF kernels analyze spherical data using generalized RBF kernels.
problem Analysis of spherical data.
method Introduced PGF kernels and a semi-parametric learning algorithm.
result PGF kernels generalize RBF kernels for spherical data.
The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.
problem Analyzing curvature properties of spherical Finsler metrics.
method Proving semi-C-reducibility and finding conditions for vanishing mean stretch curvature.
result Conditions for a general spherically symmetric Finsler metric to have vanishing mean stretch curvature.
Classifies involutions on spherical 3-manifolds.
problem Classifying involutions on spherical 3-manifolds.
method Geometric approach to conjugacy classification.
result Insights into topological properties of involutions.
The paper classifies spherically symmetric Finsler metrics as Berwaldian or Riemannian.
problem Classifying spherically symmetric Finsler metrics.
method Proving all spherically symmetric Landsberg surfaces are Berwaldian and modifying the classification of spherically symmetric Finsler metrics.
result All Berwald spherically symmetric metrics of dimension are Riemannian or given by a specific formula.
In this paper we consider the spherical slant helices in . 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.
problem Characterizing spherically symmetric metrics with scalar curvature.
method Established a curvature compatibility condition on spherically symmetric Finsler metrics and constructed a Berwald frame.
result Characterized spherically symmetric metrics with scalar curvature.
The study proves spherical polygon analogs of curve theorems, finding bounds on intersections and inflections.
problem Finding bounds on intersections and inflections for spherical polygons.
method Adapting smooth curve theorems to spherical polygons using discrete tools.
result Proves discrete analogs of four-vertex theorems for spherical polygons.
New formula for spherical polygon area via prequantization.
problem Traditional area formula for spherical polygons requires measuring angles.
method Uses prequantization to create a new formula that doesn't require angle measurement.
result New formula applicable to a wider range of degenerate curves and polygons.
Euler explored spherical geometry using trigonometric formulae and solid geometry methods.
problem Developing trigonometric formulae for spherical geometry.
method Used calculus of variations and classical solid geometry methods.
result Established trigonometric formulae and computed spherical triangle areas.
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…
Paper relaxes symmetry conditions for universal feature selection in noisy data.
problem Feature selection in noisy data with weak symmetry.
method Developed a universal feature selection framework using singular value decomposition of canonical dependence matrix.
result Selected features achieve asymptotically optimal error exponents up to a residual term.
Kähler-Ricci flow on spherical Fano manifolds converges to a soliton.
problem Analyzing the behavior of Kähler-Ricci flow on spherical Fano manifolds.
method Gromov-Hausdorff limit and torus degeneration.
result The limit of Kähler-Ricci flow on spherical Fano manifolds is a spherical Fano variety with a Kähler-Ricci soliton.