arXiv research

Study cash-subadditive risk measures without quasi-convexity.

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

Develops risk measures for markets with constraints and costs.

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

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.

It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree -1 homogeneous functions of principle curvatures in the Euclidean space. In this article, we prove that the round sphere is rigid in much stronger sens…

Proves smoothness and star-shapedness of weak IMCF solutions in hyperbolic space.

Introduces Star-Shaped deviation measures for risk analysis.

Algorithm achieves optimal regret for unknown Lipschitz convex losses.

New star-shaped acceptability indexes generalize existing methods.

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.

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…

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…

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.

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.

Designs adaptive controller for networked control systems with wireless data transmission.

In 1998 Smoczyk [Smo98] showed that, among others, the blowup limits at singularities are convex for the mean curvature flow starting from a closed star-shaped surface in $\mathbf{R}^3$. We prove in this paper that this is true for the mean curvature flow of star-shaped hypersurfaces in $\mathbf{R}^{n+1}$ in arbitrary …

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

A star-like isotopy for oriented links in 3-space is an isotopy which uses only Reidemeister II moves with opposite orientations and Reidemeister III moves with alternating orientations when checking the strands clockwise (or anticlockwise). We define a link polynomial derived from the Jones polynomial which is, in gen…

Machine learning helps create accurate models of neutron star postmerger signals.

Paper characterizes star-shaped risk measures and their properties.

Paper introduces a new $G^\star$ regret measure for online convex optimization with smooth losses.

Obstructions found for closed Fedosov star products on symplectic and Kähler manifolds.

We propose a new STAcked and Reconstructed Graph Convolutional Networks (STAR-GCN) architecture to learn node representations for boosting the performance in recommender systems, especially in the cold start scenario. STAR-GCN employs a stack of GCN encoder-decoders combined with intermediate supervision to improve the…

Injective flows for star-like manifolds improve variational inference efficiency.