A method classifies image-sets using convex cones based on CNN features.
problem Image-set classification using CNN features.
method Modeling CNN features as convex cones and measuring geometric similarity.
result Enhanced classification through discriminant space maximization of between-class variance.
Fast algorithm recovers principal eigenvector from noisy matrices.
problem Recovering the first principal eigenvector from noisy positive semidefinite matrices.
method Cone projected power iteration algorithm.
result Achieves polynomial time complexity and small error for certain convex cones.
The study finds billiard trajectories with infinitely many reflections in certain cones.
problem Existence of billiard trajectories with infinitely many reflections.
method Analysis of C3 convex cones and elliptic cones in R3. result Existence of C2 convex cones with billiard trajectories having infinitely many reflections. dboost optimizes prediction models for convex cone problems.
problem Optimizing prediction models for decision-making.
method Gradient boosting with implicit differentiation for convex quadratic cone programming.
result dboost reduces out-of-sample decision regret.
Algorithm for exact partitioning of high-order models using convex tensor relaxation.
problem Exact partitioning of high-order models.
method Defining a general class of m-degree Homogeneous Polynomial Models, relaxing the high-order combinatorial problem to a convex conic form problem, defining the Carathéodory symmetric tensor cone, and constructing a primal-dual certificate. result The solution of the convex relaxation is correct and provides a statistical upper bound for exact partitioning.
Study proves radial symmetry in convex cones using subharmonic functions.
problem Proving radial symmetry in convex cones with boundary conditions.
method Using maximum principle and integral identities for subharmonic functions.
result Proves radial symmetry and Serrin-type results for partially overdetermined problems.
CoNES optimizes blackbox functions using convex optimization and information geometry.
problem Optimizing high-dimensional blackbox functions efficiently.
method Formulated as a convex program that adapts evolutionary strategies gradient estimates.
result Vastly outperforms conventional blackbox optimization methods on benchmarks and MuJoCo tasks.
Study coning totally geodesic boundaries of hyperbolic manifolds.
problem Understanding metrics on coned-off spaces of hyperbolic manifolds.
method Analyzing the geometric and group-theoretic properties of coned-off spaces.
result Explicit conditions for negatively curved metrics and locally convex subsets.
Smooth convergence to a sphere from cone-evolving convex hypersurfaces.
problem Smooth convergence of convex hypersurfaces to a sphere inside a cone.
method Expansion driven by the power of Gauss curvature.
result Smooth convergence to a piece of round sphere after rescaling.
Smooth convergence to a sphere from cone-shaped surfaces.
problem Evolution of surfaces inside a cone using inverse mean curvature flow.
method Inverse mean curvature flow applied to star-shaped hypersurfaces meeting a convex cone perpendicularly.
result Smooth convergence to a sphere over time.
Inverse curvature flows shape star-shaped hypersurfaces into spheres.
problem Evolution of star-shaped hypersurfaces inside a convex cone.
method Inverse curvature flows, convexity of the cone, gradient and Hölder estimates.
result Hypersurfaces converge to a round sphere as time goes to infinity.
Study on p-Laplace equation in convex cones, proving rigidity under specific conditions.
problem Overdetermined problem for p-Laplace equation in convex cones. method Established properties of capacitary potential, used P-function, isoperimetric inequality, and Heintze-Karcher inequality. result Rigidity result under orthogonal intersection assumption.
The paper provides uniform length estimates for trajectories on flat cone surfaces.
problem Estimating the length of trajectories on flat cone surfaces.
method Using self-intersection numbers and constants depending only on the flat metric, the paper focuses on convex flat cone spheres with a positive curvature gap and a fixed number of singularities.
result Uniform two-sided estimates for trajectory lengths on convex flat cone spheres are obtained.
This paper proves integrability of Birkhoff billiards inside convex cones.
problem Proving integrability of Birkhoff billiards in non-traditional shapes.
method Analyzing the billiard inside a convex cone, proving integrability using a first integral of degree two.
result The Birkhoff billiard inside a convex C3 cone is integrable. Smooths out complex shapes into simpler forms.
problem Transforming complex shapes into simpler, smooth forms.
method Perturbing minimizing hypercones and viscosity mean convex cones into smooth, properly embedded hypersurfaces.
result Properly embedded smooth minimizing hypersurfaces and self-expanders are achieved.
Study on Serrin's problem in convex cones with rigidity results and geometric inequalities.
problem Serrin's overdetermined problem in convex cones of Riemannian manifolds.
method Rigidity results, soap bubble theorem, Heintze-Karcher inequality, drift Laplacian analysis.
result Characterization of intersections of geodesic balls with cones in Riemannian manifolds.
The Lee-Gauduchon cone is a convex cone of cohomology classes for complex manifolds.
problem Understanding the Lee-Gauduchon cone for complex manifolds.
method Analyzing the Lee-Gauduchon cone as a convex cone of cohomology classes.
result The Lee-Gauduchon cone is a bimeromorphic invariant.
The paper solves area minimizing problems in special geometric cones.
problem Area minimizing problems in conformal cones.
method Defining NCM condition, proving existence of minimal graphs, solving in specific cones.
result Existence of minimal graphs in mean convex conformal cones.
The study of limit cones for multi-Fuchsian representations in (PSL2R)d.
problem Characterizing the structure of limit cones for multi-Fuchsian representations.
method Analysis of normalized multi-lengths and convex cones in R≥0d. result Different regimes of limit cones exist, with some having finite sides and others dense extremal rays.
We investigate subgroups of SL (n,Z) which preserve an open nondegenerate convex cone in real n-space and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on selfdual cones, Weyl groups of certain Kac-Moody algebras …
Compact hypersurfaces minimize area in convex cones with free boundary.
problem Finding compact hypersurfaces minimizing area in convex cones with free boundary.
method Minimizing an anisotropic area functional under a volume constraint.
result Compact hypersurfaces are contained in a Wulff-shape.
We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some …
We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition we prove that the unique compact, orientable, second order minima of the weighted area under variation…
Convex relaxations improve CNNs with fixed weights.
problem Improving CNNs with fixed weights.
method Convex relaxations for CNNs with fixed weights using second order cone programs.
result The relaxation recovers the global minimum under a planted model assumption.
If a convex body C has modular and irreducible face lattice (and is not strictly convex), there is a face-preserving homeomorphism from C to a section of a cone of hermitian matrices or C has dimension 8, 14 or 26.
New conical metrics found on toric varieties with convex cones.
problem Finding conical metrics on toric affine varieties.
method Existence result for inhomogeneous Monge-Ampere equation, transversal a priori estimates.
result Existence of conical Ricci flat Kahler metrics on Q-Gorenstein affine toric varieties.
Study convex hyperbolic cone-metrics on 3-manifold boundaries, proving unique bent realizations.
problem Convex hyperbolic cone-metrics on 3-manifold boundaries and their bent realizations.
method Alexandrov-Weyl-type problem, bent metrics, controllably polyhedral, Lipschitz topology.
result Unique bent realizations for convex hyperbolic cone-metrics on 3-manifold boundaries.
Hyperkahler manifolds with round Kahler cones have unique bimeromorphic models.
problem Existence of round Kahler cones in hyperkahler manifolds.
method Analyzing the Kahler cone and its relation to the Bogomolov-Beauville-Fujiki form.
result Maximal holonomy hyperkahler manifolds with b2>4 have deformations with round Kahler cones. The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.
problem Stochastic invariance of cones in SPDEs with jumps.
method Sufficient conditions for stochastic invariance of closed convex cones in abstract L2-spaces. result Conditions for stochastic invariance of cones are provided and analyzed.
Anti-de Sitter spacetimes embed cone-metrics as bent Cauchy surfaces.
problem Embedding cone-metrics in anti-de Sitter spacetimes.
method Proving embeddings using Fuchsian representations and GHMC spacetimes.
result Unique embeddings of cone-metrics in GHMC anti-de Sitter spacetimes.
New algorithm for online optimization over symmetric cones, unifying previous methods.
problem Online convex optimization over symmetric cones.
method Symmetric-Cone Multiplicative Weights Update (SCMWU) algorithm.
result SCMWU is a no-regret algorithm.
Affine deformations of convex cones on projective surfaces.
problem Understanding affine actions on convex cones.
method Geometric correspondence and convex tube domains.
result Quotients of convex domains are affine manifolds with convex surfaces.
We show that the cone associated with a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be consider…
Establishes convexity and coercivity of K-energy functional for complex tori.
problem Convexity and coercivity of K-energy functional for complex tori.
method Geodesics in finite energy space, cone angle perturbations, stability of coercivity.
result Openness of coercivity under cone angle perturbations and existence of cscK cone metrics.
We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of Rn. Our result applies to…
The paper extends Siegel-Veech formula to convex flat cone spheres.
problem No formula exists for flat surfaces with irrational cone angles.
method Defined a generalized Siegel-Veech transform and Siegel-Veech measure.
result The Siegel-Veech measure is absolutely continuous and piecewise real analytic.
Researchers prove zero solutions for certain p-Laplacian equations in convex cones.
problem Proving zero solutions for anisotropic Finsler p-Laplacian equations in convex cones.
method Doubling argument, blowing-up method, Liouville theorems.
result All nonnegative solutions must be zero without boundedness assumption.
Unique hyperbolic affine spheres associated with convex cones in 3D.
problem Characterizing and classifying self-associated convex cones in 3D.
method Using affine spheres, hyperbolic geometry, and differential equations.
result Complete classification of self-associated convex cones and their associated affine spheres.
Researchers find H-convex functions for Heisenberg group sets.
problem Finding H-convex functions for H-convex sets in the Heisenberg group.
method Extension of Fenchel's convex family concept, employing precise conditions.
result Conditions on set shape for existence of H-convex functions.
Study collective pricing and hedging with admissible risk exchanges forming a finitely generated convex cone.
problem Collective pricing and hedging with exchanges forming a finitely generated convex cone.
method Extend collective First Fundamental Theorem of Asset Pricing and pricing-hedging duality.
result No collective arbitrage implies the closedness of the aggregate feasibility cone.
Study of spacelike discs in Minkowski cones, proving self-similar expansion.
problem Mean curvature flow of spacelike discs in Minkowski cones.
method Analysis of parabolic boundary value problem for self-similar solutions.
result Existence of solutions rescaling to self-similarly expanding solutions.
The paper proves convexity of certain solitons and expanders in high dimensions.
problem Proving convexity of specific solitons and expanders in Rn+1. method Inspired by Spruck-Xiao and Derdziński, the paper uses geometric analysis to prove convexity.
result The paper proves the convexity of complete 2-convex translating and expanding solitons and expanders in Rn+1 for n≥3. Study vanishes L2 cohomology groups on Hessian manifolds and cones.
problem Vanishing L2 cohomology groups on Hessian manifolds and cones. method Analyzes L2 cohomology groups of Kodaira-Nakano type on complete Hessian manifolds and a regular convex cone with the Cheng-Yau metric. result Obtains vanishing theorems for L2 cohomology groups on Hessian manifolds and cones. Study convex hulls of orbits for compact groups, defining new invariants related to polynomial degrees.
problem Understanding properties of convex hulls of coadjoint orbits of compact groups.
method Introduce partial convex hulls and use them to define numerical invariants.
result Orbits with new invariants form rational convex polyhedral cones related to Littlewood-Richardson cones.
We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…
Characterizes convexity of distance functions on Riemannian manifolds.
problem Understanding convexity of distance functions on Riemannian manifolds.
method Characterization of proximal normal cones, separation theorems, and analysis of convex subsets' boundaries.
result Convexity of distance functions for various boundary conditions on Riemannian manifolds.
We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This implies, among others, a conjectured best possible inequality for the U-functional of a convex body. For both results we provide stronger versions in the sense of stability i…
Affine deformations of convex cones yield special spacetime structures.
problem Deforming divisible convex cones in affine spaces.
method Analyzing the maximal convex domains and quotient structures.
result Quotients of affine actions are MGHCC affine spacetimes.