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Gauges for quadratic gravity: the extended transverse gauge and the energy-momentum tensor of the massive spin-2 field
Matheus F. S. Alves, L. G. Medeiros, Davi C. Rodrigues
https://arxiv.org/abs/2506.10793

Gauges for quadratic gravity: the extended transverse gauge and the energy-momentum tensor of the massive spin-2 field
We study the 4D Einstein-Hilbert action extension based on the square of the curvature tensors. Analyses of gauge and perturbation modes are often done considering the Teyssandier gauge condition. Although this approach can be useful for other higher-order extensions of quadratic gravity, a generalized transverse (or Lorentz) gauge is clear and sufficient for the present case, as explained here. We provide a detailed analysis of the generalized transverse gauge condition, its residual gauge sym…

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
E. Alper Yildirim
https://arxiv.org/abs/2506.09892

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the first-order optimality conditions, a quadratic program can be formulated as an optimization problem with complementarity constraints. We investigate the effect of incorporating optimality conditions on the strength of the RLT and SDP-RLT …

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
Gabriele Codega, Anna Ivagnes, Nicola Demo, Gianluigi Rozza
https://arxiv.org/abs/2506.09830

Machine Learning-based quadratic closures for non-intrusive Reduced Order Models
In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and marginally-resolved regime, i.e. when the number of modes employed is not enough to capture the system dynamics. We propose a method to re-introduce the contribution of neglected modes through a quadratic correction term, given by the action of a quadratic operator…

On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays
Rutger van Haasteren
https://arxiv.org/abs/2506.10811 https://

On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays
Pulsar Timing Array (PTA) projects have reported various lines of evidence suggesting the presence of a stochastic gravitational wave (GW) background in their data. One key line of evidence involves a detection statistic sensitive to inter-pulsar correlations, such as those induced by GWs. A $p$-value is then calculated to assess how unlikely it is for the observed signal to arise under the null hypothesis $H_0$, purely by chance. However, PTAs cannot empirically draw samples from $H_0$. As a w…

Quadratic Extended and Unscented Kalman Filter Updates
Simone Servadio, Chiran Cherian
https://arxiv.org/abs/2506.06256 https://arxiv…

Quadratic Extended and Unscented Kalman Filter Updates
Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively, but remain linear estimators, meaning that the state estimate is a linear function of the measurement. This paper proposes a quadratic approximation of the optimal estimator, creating the Quadratic Extended and Quadratic Unscented Kalman Filter. These retain…

Maximal curves with respect to quadratic extensions over finite fields
Yves Aubry (IMATH, I2M, UTLN), Fabien Herbaut (UCA INSPE, UniCA, IMATH), Julien Monaldi (IMATH)
https://arxiv.org/abs/2506.08603

Maximal curves with respect to quadratic extensions over finite fields
We propose a detailed study of a canonical bound which relates the numbers of rational points of a curve over a finite field with that over its quadratic extension. Alternative proofs which relate to the variance enable to complete the inequality in a symmetrical way and to obtain optimal refinements. We focus on the curves reaching the bound, which we call Diophantinemaximal curves. We provide different characterizations and stress natural links with the curves which attain the Ihara bound. As…

Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature
Kazuyuki Yagasaki
https://arxiv.org/abs/2506.08046 https:/…

Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature
We study the solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature when the inverse scattering transform (IST) is applied. It is a key to solve the Schrödinger equation appearing in the Lax pair in application of the IST. We show that the Schrödinger equation is always integrable in the sense of differential Galois theory, i.e., solvable by quadrature, if and only if the meromporphic potential is reflectionless, under the condition that the potential…

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
Hongwei Mei, Rui Wang, Jiongmin Yong
https://arxiv.org/abs/2506.09337

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike properties for the optimal pairs. The key is to prove a proper convergence of the solutions to the differential Riccati equations to the algebraic Riccati equation. Even for the problems without regime switchings, our result provides a refined estimate compared to t…

Stochastic Quadratic Dynamic Programming
Vincent Guigues, Adriana Washington
https://arxiv.org/abs/2506.07314 https://arxiv.org/pdf/2…

Stochastic Quadratic Dynamic Programming
We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual Dynamic Programming (SDDP) method replacing affine cuts by quadratic cuts. We provide conditions ensuring strong convexity of the recourse functions and prove the convergence of SQDP. In the special case of a single stage deterministic problem, we call QCSC (Quadra…