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Iterative polynomial regularisation of $\text{P}_{\text{IV}}$-type: Hamiltonian systems and Newton polygons
Marta Dell'Atti, Galina Filipuk
https://arxiv.org/abs/2510.12378 …

Iterative polynomial regularisation of $\text{P}_{\text{IV}}$-type: Hamiltonian systems and Newton polygons
We study several polynomial Hamiltonian systems of $\text{P}_{\text{IV}}$-type (including the mixed case quasi-$\text{P}_{\text{IV}}$), and show that via the iterative process of polynomial regularisation, it is possible to identify the "minimal" Hamiltonian system. The selected Hamiltonian function is associated with the Newton polygon with minimal area and smallest highest total degree.

Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty
Achraf Bouhmady, Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11396

Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty
This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum differential game between a control policy and an adversarial disturbance. Within a Hamilton-Jacobi framework, the viability kernel is characterized as the zero sublevel set of a value function satisfying a constrained Hamilton-Jacobi-Bellman (HJB) equation in the vi…

🏈 Bill Belichick’s humiliating college football debut brings only schadenfreude or sadness
https://www.theguardian.com/sport/2025/sep/02/bill-belichick-unc-first-game-college-football-tcu

I need to know this guy's fedi handle asap #canada #ontario #transit

Man who took Hamilton bus on joy ride 'did a great job' driving, left no dings, say police | CBC News
He made several stops along the way, allowing passengers to get on and off, police say. He was then arrested.

Stochastic Homogenization of the Hamilton-Jacobi Equation on Manifolds
Marco Pozza, Alfonso Sorrentino
https://arxiv.org/abs/2510.11714 https://arxiv.org/p…

Stochastic Homogenization of the Hamilton-Jacobi Equation on Manifolds
This article establishes a stochastic homogenization result for the first order Hamilton-Jacobi equation on a Riemannian manifold $M$, in the context of a stationary ergodic random environment. The setting involves a finitely generated abelian group $ \mathtt{G}$ of rank $b$ acting on $M$ by isometries in a free, totally discontinuous, and co-compact manner, and a family of Hamiltonians $H: T^*M \times Ω\to \mathbb{R}$, parametrized over a probability space $(Ω, \mathbb{P})$, which are statio…

Lagrange-Hamilton geometry applied to a Lotka-Volterra dynamical system
Ana-Maria Boldeanu, Mircea Neagu
https://arxiv.org/abs/2510.09843 https://arxiv.org…

Lagrange-Hamilton geometry applied to a Lotka-Volterra dynamical system
The aim of this paper is to develop, via the least squares variational method, the Lagrange-Hamilton geometry (in the sense of nonlinear connections, d-torsions and Lagrangian Yang-Mills electromagnetic-like energy) produced by a Lotka-Volterra dynamical system, a simple model of the population dynamics of species competing for some common resource. From a geometrical point of view, the Jacobi stability of this system is discussed.

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Dylan Hirsch, Jaime Fern\'andez Fisac, Sylvia Herbert
https://arxiv.org/abs/2510.09929

Viscosity CBFs: Bridging the Control Barrier Function and Hamilton-Jacobi Reachability Frameworks in Safe Control Theory
Control barrier functions (CBFs) and Hamilton-Jacobi reachability (HJR) are central frameworks in safe control. Traditionally, these frameworks have been viewed as distinct, with the former focusing on optimally safe controller design and the latter providing sufficient conditions for safety. A previous work introduced the notion of a control barrier value function (CB-VF), which is defined similarly to the other value functions studied in HJR but has certain CBF-like properties. In this work, …

The Chico Hamilton Quartet / Elmer Bernstein, Concerto of Themes from Soundtrack of "Sweet Smell of Success". #sound
https://moochinaboutltd.bandcamp.com/track/concerto-of-…

Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation
Fanch Coudreuse
https://arxiv.org/abs/2510.09231 https://arxiv.org/pdf/2510.0…

Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation
We establish a version of the Li--Yau--Hamilton inequality for the Granular-Medium equation on the torus, both at the PDE level and for its time-discrete approximation given by the JKO scheme. We then apply this estimate to derive further quantitative results for the continuous and discrete JKO flows, including Lipschitz and $L^\infty$ bounds, as well as a quantitative Harnack inequality. Finally, we use the regularity provided by this estimate to show that the JKO scheme for the Fokker--Planck…