Study on functional ellipsoids to decompose the identity.
problem Decompose the identity for functional ellipsoids.
method Construct a decomposition similar to Fritz John's theorem.
result Developed a new approach to functional ellipsoids.
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.
169,181 papers · 148 categories
Trend · papers per month
48 results for “John's ellipsoid”
John's Walkstat.ML
John's walk uses John's ellipsoids for uniform sampling from convex bodies.
problem Drawing uniform random samples from convex bodies efficiently.
method Affine-invariant random walk using John's ellipsoids for proposal distribution.
result The random walk mixes in steps from a warm start.
Using an idea of Voronoi in the geometric theory of positive definite quadratic forms, we give a transparent proof of John's characterization of the unique ellipsoid of maximum volume contained in a convex body. The same idea applies to the 'hard part' of a generalization of John's theorem and shows the difficulties of…
The paper applies a capillary John ellipsoid theorem to solve capillary curvature problems.
problem Solving capillary curvature problems in Euclidean half-spaces.
method Applying a capillary John ellipsoid theorem to derive non-collapsing estimates and gradient estimates.
result Established existence of solutions to capillary curvature problems in certain ranges of and .
A Pu-Bonnesen inequalitymath.MG
The paper proves a Bonnesen-type inequality for the real projective plane.
problem Proving an inequality for the real projective plane.
method Using Pu's systolic inequality, John ellipsoids, and Pogorelov's rigidity theorem.
result Generalized Pu's systolic inequality for positively-curved metrics.
New algorithm for linear optimization with adaptive corruption.
problem Stochastic linear optimization under adversarial corruption.
method Algorithm uses Löwner-John's ellipsoid for exploration and divides time into epochs.
result Regret increases linearly with corruption amount.
On the approximation of convex bodies by ellipses with respect to the symmetric difference metricmath.MG
Given a centrally symmetric convex body and a positive number , we consider, among all ellipsoids of volume , those that best approximate with respect to the symmetric difference metric, or equivalently that maximize the volume of : these are the maxi…
New MCMC algorithms speed up sampling from polytope distributions.
problem Sampling from uniform distributions over polytopes efficiently.
method Vaidya walk and John walk based on interior point methods.
result Vaidya walk mixes significantly faster than Dikin walk.
Defines John-Nirenberg radius for collapsing conformal metrics and proves a convergence theorem.
problem Analyzing collapsing conformal metrics in a fixed conformal class.
method Defining John-Nirenberg radius and proving convergence using curvature conditions.
result The John-Nirenberg radius is bounded below by a positive constant for collapsing conformal metrics.
Paper proves existence and gives construction of Symphonic map between ellipsoids.
problem Existence and construction of Symphonic map between ellipsoids.
method Geometric construction using Hopf map.
result Existence and construction of Symphonic map from ellipsoid to ellipsoid.
CTEF fits ellipsoids to noisy data in any dimension.
problem Fitting ellipsoids to noisy data in arbitrary dimensions.
method Uses the Cayley transform to fit ellipsoids.
result CTEF outperforms other methods, especially when data are not uniformly distributed.
The paper uses Seshadri constants to construct symplectic ellipsoid embeddings.
problem Constructing symplectic embeddings of ellipsoids.
method Exploring weighted blow-ups and Seshadri constants to demonstrate symplectic embeddings.
result Illustrates constructions of ellipsoid fillings and embeddings.
Conway's drum quiltsmath.GT
John Conway created pairs of domains that sound the same for a special kind of music.
problem Creating domains that sound the same for a special kind of music.
method Using his theory of quilts, Conway developed pairs of glueing diagrams.
result Conway's pairs of domains are isospectral for the Laplace operator.
New minimal discs and annuli found in ellipsoids.
problem Constructing minimal surfaces in ellipsoids.
method Equivariant variational methods.
result At least three distinct embedded free boundary minimal annuli in ellipsoids.
The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.
problem Constructing reliable confidence regions for linear regression with finite sample sizes and general noise distributions.
method The paper introduces the SPS EOA algorithm to create non-asymptotically guaranteed confidence ellipsoids for linear regression problems.
result The sizes of SPS outer ellipsoids are shown to decrease at the optimal rate for linear regression problems.
We discuss Darboux-Staude type of thread configurations for the ellipsoid similar to Chasles-Graves type of thread configurations for the ellipse. These threads are formed by rectilinear segments, geodesic and line of curvature segments on the considered ellipsoid and with tangents tangent to the given ellipsoid and a …
Jacobi's solution for geodesics on a triaxial ellipsoidphysics.geo-ph
Jacobi solved geodesics on triaxial ellipsoids.
problem Finding the shortest path on a triaxial ellipsoid.
method Numerical evaluation of integrals and solving coupled equations.
result Solution for geodesics on triaxial ellipsoids.
Study finds many nonplanar minimal spheres in elongated ellipsoids.
problem Existence of nonplanar minimal spheres in elongated ellipsoids.
method Global bifurcation techniques to establish existence and quantify number.
result Arbitrarily many nonplanar minimal spheres exist in elongated ellipsoids.
Study smoothings of singular intersections of ellipsoids.
problem Smooth singular intersections of ellipsoids.
method Generic singularities of coaxial intersections of ellipsoids studied.
result Special attention to 3D case.
Optimizes ellipsoids for uncertainty regions in parameter estimation.
problem Learning minimal volume uncertainty ellipsoids for parameter estimation.
method Differentiable optimization approach using neural networks to approximate optimal ellipsoids.
result Approximately computed ellipsoids are smaller and more accurate than existing methods.
The paper finds a geometric way to minimize a convex function to construct isotropic measures.
problem Constructing isotropic measures in convex bodies.
method Minimizing a convex function in a high-dimensional space.
result Geometric interpretation of the minimizer as a derivative.
Discrete analogues of ellipsoids with preserved circular cross sections.
problem Constructing discrete analogues of ellipsoids with preserved geometric properties.
method A novel discretization procedure to create discrete analogues of ellipsoids composed of planar quadrilaterals.
result Discrete analogues of ellipsoids have preserved circular cross sections and can be deformed.
Ellipsoids host infinitely many minimal tori, bifurcating from a 2-torus orbit.
problem Minimal tori in ellipsoids.
method Analyzing 3D ellipsoids invariant under a 2-torus action.
result Infinitely many distinct minimal tori bifurcate from a 2-torus orbit.
We develop an efficient algorithm to find confidence ellipsoids with volume guarantees in high dimensions.
problem Finding robust confidence ellipsoids in high-dimensional data.
method Polynomial time algorithm using primal-dual structure and geometric Brascamp-Lieb inequality.
result Algorithm finds ellipsoids within a volume factor of best -conditioned ellipsoid.
Study smoothings of ellipsoid intersections with singularities.
problem Smooth singular intersections of ellipsoids.
method Study 3D manifolds with singularities as small covers of Coxeter polyhedral orbifolds.
result Introduce -pyramitoid to generalize -pyramids.
Self-focal points on ellipsoids of dimension 3 or higher are rare.
problem Existence of self-focal points on Riemannian manifolds of dimension 3 or higher.
method Analyzing geodesics and umbilic points on ellipsoids of various dimensions.
result Ellipsoids of dimension 3 or higher with at least 4 distinct axes have no self-focal points.
Geodesics on an arbitrary ellipsoid of revolutionphysics.geo-ph
Geodesic algorithms extended to arbitrary ellipsoids.
problem Computing geodesics on ellipsoids of varying eccentricity.
method Implementation of geodesic algorithms using elliptic integrals and discrete sine transform.
result Achieved high accuracy (close to machine precision) for geodesic computations.
Ellipsoids approach Gaussian distribution in high dimensions.
problem Understanding convergence of high-dimensional ellipsoids to Gaussian spaces.
method Proof of convergence in Gromov's concentration topology.
result Solid ellipsoids converge to Gaussian space in high dimensions.
The paper studies the number of normals to ellipsoids and their intersections with caustics.
problem The number of normals to an ellipsoid passing through a given point.
method Intersection points of the ellipsoid and its caustics are used to study the problem in 3D space.
result The number of normals is dependent on the position of the given point with respect to the caustics of the ellipsoid.
The study finds conditions for minimal spheres into ellipsoids using eigenfunctions.
problem Conditions for branched minimal immersions of spheres into ellipsoids to be embedded.
method Using eigenfunctions with respect to a critical metric, the study provides sufficient conditions for embeddings and constructions of non-planar minimal spheres.
result Conditions for embeddings and constructions of non-planar minimal spheres using eigenfunctions.
Markov staircasesmath.SG
Study Markov staircases in symplectic embeddings of rational homology ellipsoids.
problem Symplectic embeddings of rational homology ellipsoids into the complex projective plane.
method Analysis of almost toric fibrations and Hamiltonian isotopies.
result Existence of an infinite staircase for each Markov triple.
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and space-like geodesics and invariant 1-form on the space of null geodesics. We prove a…
Closed-Form Parametric Equation for the Minkowski Sum of Ellipsoids in and Associated Volume Boundsmath.MG
Derives exact formula for Minkowski sum of ellipsoids in N-space.
problem Finding volume bounds for Minkowski sum of ellipsoids.
method Closed-form parametric equation derivation and volume bounds calculation.
result Upper and lower volume bounds for Minkowski sum of ellipsoids.
We study the ellipticity and the ``Nekhoroshev stability'' (stability properties for finite, but very long, time scales) of the Riemann ellipsoids. We provide numerical evidence that the regions of ellipticity of the ellipsoids of types II and III are larger than those found by Chandrasekhar in the 60's and that all Ri…
Classifies real algebraic curves on a quadric ellipsoid of specific degree.
problem Classifying real algebraic curves of bidegree (5,5) on the quadric ellipsoid.
method Reduction to curves in the second Hirzebruch surface, combining classical construction methods on toric surfaces.
result Previously known restrictions form a complete system for this bidegree.
New framework for better mapping of surfaces onto ellipsoids.
problem Mapping genus-0 closed surfaces onto spheres results in large distortion.
method Combining conformal and quasi-conformal mappings onto ellipsoids.
result Achieved a variety of ellipsoidal parameterizations with bijectivity.
Study eigenvalues of ellipsoids near a sphere, comparing to sphere's.
problem Analyzing changes in Laplacian eigenvalues for ellipsoids near a sphere.
method Comparison with standard Euclidean unit sphere, under Gaussian curvature condition.
result Eigenvalues of ellipsoids near a sphere, with comparison to sphere's.
Infinite families of maps found on ellipsoids in various dimensions.
problem Finding harmonic self-maps on ellipsoids in multiple dimensions.
method Analyzing ellipsoids with specific conditions and proving the existence of infinitely many harmonic maps.
result Infinite families of harmonic self-maps exist on ellipsoids under given conditions.
We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyz…
VC dimension of ellipsoidsmath.CO
We will establish that the VC dimension of the class of d-dimensional ellipsoids is (d^2+3d)/2, and that maximum likelihood estimate with N-component d-dimensional Gaussian mixture models induces a geometric class having VC dimension at least N(d^2+3d)/2. Keywords: VC dimension; finite dimensional ellipsoid; Gaussian m…
We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian -manifold having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of …
Proves existence of non-planar minimal disks in ellipsoids.
problem Existence of non-planar minimal disks in ellipsoids.
method Optimization of Steklov eigenvalues and critical metrics.
result Existence of embedded non-planar free boundary minimal disks.
The paper describes the CR umbilical locus of a real ellipsoid in complex space.
problem Characterizing the CR umbilical locus of a real ellipsoid in complex space.
method Analyzing the set of points where the ellipsoid can be osculated by a biholomorphic image of the sphere up to 6th order.
result The CR umbilical locus is the union of stable curves and a non-trivial real variety defined by sextic equations.
Paper proves existence of conjugate points on ellipsoids but not on spheres.
problem Existence of conjugate points in incompressible Euler flows.
method Formulated a differential-geometric criterion (M-criterion) and analyzed flows on spheres and ellipsoids.
result Zonal flows on ellipsoids can satisfy M-criterion, while not on spheres.
Absolute Return Volatilityq-fin.ST
The use of absolute return volatility has many modelling benefits says John Cotter. An illustration is given for the market risk measure, minimum capital requirements.
The paper solves the problem of fitting an ellipsoid to random points efficiently.
problem Finding an ellipsoid that passes through random Gaussian points.
method Constructing a fitting ellipsoid using a decomposition of a random matrix and graph matrix theory.
result The ellipsoid fitting problem transitions from feasible to infeasible at a sharp threshold of .
We use ellipsoids to solve power system voltage regulation problems.
problem Voltage regulation in power systems under uncertainty.
method Tractable ellipsoidal approximation for chance constrained optimizations.
result Efficiently trained machine learning model approximates uncertainty region.
Study the spectrum of Poincaré operator in triaxial ellipsoids.
problem Spectrum of the Poincaré operator in triaxial ellipsoids.
method Microlocal analysis of partial differential equations and polynomial vector fields.
result Polynomial eigenvectors and large-degree asymptotics of the operator.