Tootfinder

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach
P. T. Kirakosiants, D. A. Valerev, M. A. Vasiliev
https://arxiv.org/abs/2506.16634

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach
The recently proposed differential homotopy approach to the analysis of nonlinear higher spin theory is developed. The Ansatz is extended to the form applicable in the second order of the perturbation theory and general star-multiplication formulae are derived. The relation of the shifted homotopy and differential homotopy formalisms is worked out. Projectively-compact spin-local quadratic (anti)holomorphic vertices in the one-form sector of higher-spin equations are obtained within the differe…

Approximation of risk-averse optimal feedback control
Philipp A. Guth, Karl Kunisch
https://arxiv.org/abs/2508.15618 https://arxiv.org/pdf/2508.15618

Approximation of risk-averse optimal feedback control
The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear entropic risk measure. A sequential quadratic programming scheme is derived that iteratively solves linear quadratic subproblems obtained through second-order Taylor expansions of the objective functional, with each subproblem re-centered at the previous iterate. …

Smooth Games of Configuration in the Linear-Quadratic Setting
Jesse Milzman, Jeffrey Mao, Giuseppe Loianno
https://arxiv.org/abs/2507.16611 https://…

Smooth Games of Configuration in the Linear-Quadratic Setting
Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is existing literature on the parametrization of dynamic games, little research examines this parametrization from a strategic perspective where each agent's configuration choice is influenced by the decisions of others. In this work, we introduce the concept of a ga…

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Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
Roger Anderson Hurtado
https://arxiv.org/abs/2506.15123 https://arxiv.or…

Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
We study the gravitational potential arising from static, spherically symmetric sources in a modified gravity theory described by a quadratic $f(R)$ model. The linearized field equations lead to a fourth-order differential equation, whose solution includes Newtonian and Yukawa-like terms. Imposing regularity at the origin and asymptotic flatness fixes all integration constants, making the potential fully determined by the mass distribution. We analyze classical profiles such as Plummer, Hernqui…

Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus
Ahmed Abdalmuhsin Abdalsahib
https://arxiv.org/abs/2507.13402 https://…

Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps, including linear, quadratic, cubic, and higher-order forms. Using elementary techniques from differentiation and integration, the approach produces polynomial expressions that represent total sums, even when each term is raised to a positive integer power. As a resu…

The invisible hand as an emergent property: a gradient flow approach
Giorgio Fabbri, Davide Fiaschi, Cristiano Ricci
https://arxiv.org/abs/2508.14498 https://

The invisible hand as an emergent property: a gradient flow approach
We develop a general equilibrium model in which, at each instant, a short-run competitive equilibrium arises. Heterogeneity in factor allocation generates differential profit rates across sectors, prompting firms to move between them under myopic profit-seeking behaviour, subject to quadratic reallocation costs. The aggregate dynamics of the economy can be formalised as a gradient flow in a Wasserstein space, starting from a partial differential equation that describes the reallocation of firms…

Replaced article(s) found for eess.SY. https://arxiv.org/list/eess.SY/new
[1/1]:
Sample Complexity of the Linear Quadratic Regulator: A Reinforcement Learning Lens

Near optimal controls for partially observed stochastic linear quadratic problems
Jingrui Sun, Jiaqiang Wen, Jie Xiong, Wen Xu
https://arxiv.org/abs/2506.11778

Near optimal controls for partially observed stochastic linear quadratic problems
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the diffusion term of the state equation, the circular dependence between the control process and the filtration generated by the observation, and the observation process contains an unbounded drift term. We address these difficulties by first restricting the contro…

The AdS Perspective on the Nonlinear Tails in Black Hole Ringdown
Alex Kehagias, Antonio Riotto
https://arxiv.org/abs/2506.14475 https://

The AdS Perspective on the Nonlinear Tails in Black Hole Ringdown
Black holes gradually settle into their static configuration by emitting gravitational waves, whose amplitude diminish over time according to a power-law decay at fixed spatial locations. We show that the nonlinear tails in the presence of a quadratic source, which have been recently found to potentially dominate over the linear ones, can be simply derived from the AdS$_2$$\times$S$^2$ spacetime perspective with their amplitudes being related to the Aretakis constants.