arXiv research

We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeli…

Semiparametric STAR model improves mental health data analysis.

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…

The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies in convex geometry.

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

The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is integrable if the local differential invariants of a solution to the curve flow evolve according to a soliton equation. In this paper, we sho…

Researchers create a star product on a Grassmannian with separation of variables.

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

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 …

Neural networks can achieve optimal sample complexity for learning single-index models.

This paper connects geometric diagrams to spherical T-duality.

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

Study shows computational and statistical gaps in Gaussian Single-Index Models.

Introduces Star-Shaped deviation measures for risk analysis.

A new clustering method handles uncertain covariates efficiently.

Simplifies F-measure for better interpretability.

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.

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 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.

Transformer with denoising diffusion improves probabilistic density estimation.

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.

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…

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

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…

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…

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.

Introduces Star-Shaped DDPMs for non-Gaussian distributions.

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

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…

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

Researchers create initial data for multiple collapsing boson stars.