arXiv research

Estimates how many times a star appears due to gravitational lensing.

New lower bound shows bandit convex optimization is harder than previously thought.

We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective first-class constraint (gauge) system equivalent to the original second-class o…

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low rank matrix $Θ^\star$ with a second matrix $Γ^\star$ endowed with a complementary …

Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.

STAR improves equivariant and invariant representation learning by routing projection heads.

Paper proposes Sp-GD for sparse max-affine regression with theoretical guarantees.

Introduces Star-Shaped deviation measures for risk analysis.

Gaia will obtain astrometry and spectrophotometry for essentially all sources in the sky down to a broad band magnitude limit of G=20, an expected yield of 10^9 stars. Its main scientific objective is to reveal the formation and evolution of our Galaxy through chemo-dynamical analysis. In addition to inferring position…

The paper explores graphons of line graphs from sparse finite graphs.

Algorithm achieves optimal regret for unknown Lipschitz convex losses.

New star-shaped acceptability indexes generalize existing methods.

Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.

We analyze optimal weighted ridge regression in overparameterized linear models.

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on $M$ …

Classifies star products on Lie algebroid duals and extends to projectable quantizations.

New algorithm for robust density estimation in corrupted data.

New set-valued star-shaped risk measures introduced for better risk assessment.

Flow turns star-shaped curves into circles.

The paper studies dynamic star-shaped risk measures and their representation.

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\s…

Study star products on Poisson manifolds compatible with reduction.

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.

Deform moment map on symplectic connections using star product algebras.

Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.

New partition designs reduce star discrepancy in high-dimensional sampling.

This paper optimizes Bayesian estimation for log-concave models using Langevin Monte-Carlo.

We compare the star surgery operations introduced in [KS] to the generalized rational blow-down. We show that star surgery shares the properties that make rational blow-down useful for constructions of small exotic symplectic 4-manifolds. Then we show that star surgery operations provide a strictly more general class o…

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we ca…

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this …

Improved SGD learning for single index models reduces sample complexity.

Let $K$ be a nontrivial knot in $S^{3}$ and $t(K)$ its tunnel number. For any $(p\geq 2,q)$-slope in the torus boundary of a closed regular neighborhood of $K$ in $S^{3}$, denoted by $K^{\star}$, it is a nontrivial cable knot in $S^{3}$. Though $t(K^{\star})\leq t(K)+1$, Example 1.1 in Section 1 shows that in some cas…

New methods for private statistical inference under local differential privacy.

The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.

This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.

Given a bordified space, Karlsson defines an incidence geometry of stars at infinity. These stars and their incidence are closely related to well-understood objects when the space is hyperbolic, CAT(0), or a bounded convex domain with the Hilbert metric. A question stemming from Karlsson's original paper was whether or…

The paper proves inequalities for star-shaped and $F$-mean convex hypersurfaces in $\mathbb{R}^{n+1}$.

We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection introduced by the first author. We establish a necess…

Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a variety of deep neural networks. However, there is still a lack of understanding on how and why SGD can train these complex networks towards a global minimum. In this study, we establish the convergence of SGD to a global minimu…

Constructs non-unital monoidal category of contact manifolds and Legendrian correspondence calculus

Sharp inequalities for star bodies in 2D space.

The paper characterizes law-invariant star-shaped risk measures.

The study counts geodesics on curved surfaces with specific intersections.

This study uses deep learning to infer stellar parameters from short TESS and K2 observations.

Introduces Star-Shaped DDPMs for non-Gaussian distributions.

The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.

Study quantization schemes on Kähler manifolds linking star products and BV quantizations.

Researchers create initial data for multiple collapsing boson stars.