Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
L. Manivel, M. Michałek, Leonid Monin, Tim Seynnaeve, Martin Vodivcka
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引用次数: 22

Abstract

We establish connections between: the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert calculus for complete quadrics. We prove a conjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. We also prove a conjecture by Nie, Ranestad and Sturmfels providing an explicit formula for the degree of SDP. The interactions between the three fields shed new light on the asymptotic behaviour of enumerative invariants for the variety of complete quadrics. We also extend these results to spaces of general matrices and of skew-symmetric matrices.
完全二次:舒伯特演算高斯模型和半定规划
我们建立了线性集中模型的最大似然度(ml度)、半定规划的代数度(SDP)和完全二次曲线的Schubert微积分之间的联系。我们证明了sturmfeles和Uhler关于ml度的多项式性的一个猜想。我们还证明了Nie, Ranestad和Sturmfels的猜想,提供了SDP程度的显式公式。这三个场之间的相互作用揭示了各种完全二次型的枚举不变量的渐近行为。我们也将这些结果推广到一般矩阵和偏对称矩阵的空间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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