Tootfinder

On quadratic persistence and Pythagoras numbers of totally real projective varieties
Jong In Han, Jaewoo Jung, Euisung Park
https://arxiv.org/abs/2506.13247

On quadratic persistence and Pythagoras numbers of totally real projective varieties
In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekherman et al. in arXiv:1902.02754, we extend their characterizations of arithmetically Cohen-Macaulay varieties with next-to-maximal quadratic persistence to arbitrary case. Our main result classifies totally real non-aCM varieties of codimension $c$ and degree $d$ that exhibit next-to-maximal quadratic persistence in t…

A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
Zibo Zhao
https://arxiv.org/abs/2506.13078 https://ar…

A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided into small tetrahedrons, and by employing the change of variables formula, the approach yields an algorithm requiring only one-dimensional root finding and standard Gaussian quadrature. The resulting quadrature scheme guarantees strictly positive weights and …

Automatic Generation of Explicit Quadratic Programming Solvers
Maximilian Schaller, Daniel Arnstr\"om, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.11513

Automatic Generation of Explicit Quadratic Programming Solvers
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a so…

Thermodynamics of FLRW universe in Quadratic Gravity
Navid Safarzadeh Ilkhchi, Amin Rezaei Akbarieh, Yaghoub Heydarzade
https://arxiv.org/abs/2507.12055 ht…

Thermodynamics of FLRW universe in Quadratic Gravity
In this paper, we investigate the thermodynamic aspects of quadratic gravity in a $D$-dimensional Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. First, we derive the field equations and the effective energy-momentum tensor for quadratic gravity. Then, using these equations, we obtain the generalized Misner-Sharp energy within the framework of this model. We consider the thermodynamic behavior of the apparent horizon and derive the equations of state related to the pressure, temperature, a…

Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity
Ichiro Oda
https://arxiv.org/abs/2507.10712 https://

Vanishing Metric Commutation Relation and Higher-derivative De Donder Gauge in Quadratic Gravity
We show that the equal-time commutation relations (ETCRs) among the time derivatives of the metric tensor identically vanish in the higher-derivative de Donder gauge as well as the conventional de Donder gauge (or harmonic gauge) for general coordinate invariance in the manifestly covariant canonical operator formalism of quadratic gravity. These ETCRs provide us with the vanishing four-dimensional commutation relation, which implies that the metric tensor behaves as if it were not a quantum op…

Coxeter matrices and homological quadratic forms of $\boldsymbol{n}$-hereditary algebras
Raziyeh Diyanatnezhad, Alireza Nasr-Isfahani
https://arxiv.org/abs/2506.13136

Coxeter matrices and homological quadratic forms of $\boldsymbol{n}$-hereditary algebras
We study the Coxeter matrices and the homological quadratic forms of $n$-hereditary algebras within the framework of higher dimensional Auslander--Reiten theory. Let $Λ$ be a finite dimensional $n$-hereditary algebra with the Coxeter matrix $Φ$ and the homological quadratic form $χ$. We prove that if $Λ$ is $n$-representation finite, then there exists a positive integer $d$ such that $Φ^d=1$. In the case $n$ is an odd number, we show that if there exists a positive integer $d$ such that $Î…

Rate of metastability of an iterative algorithm for quadratic optimization
Paulo Firmino
https://arxiv.org/abs/2506.11342 https://arx…

Rate of metastability of an iterative algorithm for quadratic optimization
In this paper, relying on methods from proof mining, we provide a quantitative analysis of a theorem due to Xu, stating that an iteration strongly converges to the solution of a well known quadratic optimization problem. Rates of metastability and some rates of asymptotic regularity were obtained. We get quadratic rates of asymptotic regularity for particular sequences.

Turnpike properties in linear quadratic Gaussian N-player differential games
Asaf Cohen, Jiamin Jian
https://arxiv.org/abs/2507.11632 https://

Turnpike properties in linear quadratic Gaussian N-player differential games
We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic $N$-player game with Gaussian initial data. By analyzing convergence toward the corresponding ergodic game, we establish exponential convergence estimates between the solutions of the finite-horizon Riccati system and the associated algebraic Riccati system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a tu…

SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
P. C. N. Verheijen, D. Goswami, M. Lazar
https://arxiv.org/abs/2506.11608 https://…

SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM
In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that penalizes each constraint individually and performs weight updates at every ADMM iteration. We provide a numerical stability analysis, methods for parameter selection and infeasibility detection. The algorithm is implemented in c with efficient linear algebra pac…

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Weijian Li, Panagiotis Kounatidis, Zhong-Ping Jiang, Andreas A. Malikopoulos
https://arxiv.org/abs/2506.12596

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing the robustness of derivative-free methods for solving an infinite-horizon LQR problem. To be specific, we estimate policy gradients by cost values, and study the effect of perturbations on the estimations, where the perturbations may arise from function approx…