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.
Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
Geodesic spheres in certain symmetric spaces are quantitatively stable under small perturbations.
Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant's treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the fam…
New approach to quantum knot invariants using perturbed Gaussian generating functions.
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…
Extended Rank-One Theorem to special metric spaces.
In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.
Constructs explicit p-harmonic functions on specific Lie groups.
The study establishes uncertainty principles on harmonic manifolds of rank one.
We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recove…
Classifies foliations on specific symmetric spaces.
Develops Hilbert geometries and characterizes their isometries.
We give a positive answer to the Chavel's conjecture [J. Diff. Geom. 4 (1970), 13-20]: a simply connected rank one normal homogeneous space is symmetric if any pair of conjugate points are isotropic. It implies that all simply connected rank one normal homogeneous space with the property that the isotropy action is var…
New method improves on existing algorithms for rank-one bandits.
Improved stability for matrix recovery from rank-one measurements.
Classifies rank-one submanifolds in Euclidean space.
No Einstein hypersurfaces found in Damek-Ricci spaces.
New insights into compact rank-one ECS manifolds, proving they are bundles over circles.
Study closed manifolds with rank one ray structures, proving completeness or covering properties.
Compact rank one symmetric spaces are rigid under certain curvature conditions.
In this paper we show that if the limit set is not small ,marked length spectrum determines geometric structure of rank one locally symmetric manifolds.
We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.
We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations, we propose an easy-to-use, end-to-end trainable, low-rank regularizer (LR) that…
We show that cocompact lattices in rank one simple Lie groups of non-compact type distinct from SO(2m,1) (m>0) contain surface subgroups.
Researchers describe the metric structure of compact ECS manifolds.
Novel algorithm for Markov decision processes using rank-one approximation.
Rank-one measurements limit feasible sets for low-rank PSD matrices.
In this paper, based on research on rank-one isometries by W.Ballmann and M.Brin and recent research on rank-one isometries of Coxeter groups by P.Caprace and K.Fujiwara, we study a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter g…
New random walk results on rank one symmetric spaces.
We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.
We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z_2-coefficients.
The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.
Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.
The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.
Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.
Let M be a geometrically finite rank one locally symmetric manifolds. We prove that the spectrum of the Laplace operator on M is finite in a small interval which is optimal.
We prove some estimates of the volumes of the sets of translation surfaces of unit area having several independent small saddle connections in a rank one affine submanifold.
In this paper we study the equidistribution of expanding horospheres in infinite volume geometrically finite rank one locally symmetric manifolds and apply it to the orbital counting problem in apollonian sphere packing.
We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.
New rigidity theorem for product of lattices.
New method unifies and formalizes data partitioning using a single vector.
Completes the space of vector-valued one-forms on manifolds.
We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface are not dense in the set of probability measures invariant by the geodesic flow. F…
Study shows how fast a specific matrix completion method works.
We prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given four-manifold. In a previous article, dg-ga/9710032, we proved transversality using an extension of the hol…
ROIPCA and fROIPCA are online PCA algorithms using rank-one updates.