arXiv research

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…

The study constructs symplectic 4-manifolds with exotic structures.

Conjecturally, the only knots in $S^3$ with non-integer surgeries producing Seifert fibered spaces are torus knots and cables of torus knots. In this paper, we make progress on the associated realization problem. Let $Y$ be a small Seifert fibered space arising by $p/q$-surgery on a knot in $S^3$, where $p/q$ is positi…

We define a new 4-dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern's rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective space blown-up eight times, seven times, and six times. We also show how this operatio…

This paper connects geometric diagrams to spherical T-duality.

From a pseudo-triangulation with $n$ tetrahedra $T$ of an arbitrary closed orientable connected 3-manifold (for short, {\em a 3D-space}) $M^3$, we present a gem $J '$, inducing $\IS^3$, with the following characteristics: (a) its number of vertices is O(n); (b) it has a set of $p$ pairwise disjoint couples of vertices …

We define a new 4-dimensional symplectic cut and paste operations arising from the generalized star relations $(t_{a_0}t_{a_1}t_{a_2} \cdots t_{a_{2g+1}})^{2g+1} = t_{b_1} t_{b_2}^{g}t_{b_3}$, also known as the trident relations, in the mapping class group $Γ_{g,3}$ of an orientable surface of genus $g\geq1$ with $3$ b…

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.

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.

Paper disproves symmetry of stars at infinity in a specific graph.

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.

CasVAE outperforms supervised methods for star-galaxy classification.

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

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

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.

In this final part of a 3-part paper we introduce the pair of "wings" of the abstract PL-colored complexes $\mathcal{H}_{m}^\star$, described in the second paper. The wings, via a weight enhanced Tutte's barycentric embedding of a planar map, produce the unexpected reformutation of a 3-dimensionl problem into a 2-dimen…

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.

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

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

Sharp inequalities for star bodies in 2D space.

The study counts geodesics on curved surfaces with specific intersections.

Introduces Star-Shaped DDPMs for non-Gaussian distributions.

Study tunnel numbers of cable knots and their companions, proving new bounds and constructing examples.

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 linear bandits.

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

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

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…

Paper characterizes star-shaped risk measures and their properties.