the Equation of State
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Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems
Announce Type: cross Abstract: Bayesian inverse problems constrained by state equations are often sampled in a full parameter-state space by penalising the residual, rather than in a reduced space where the state is eliminated. We show that these formulations are not automatically equivalent as posterior measures. For finite-dimensional discretisations of equality-constrained inverse problems, assume the state equation \(c(\theta,u)=0\) has a unique solution \(u=G(\theta)\) and nonsingular...
Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs
arXiv:2604.03399v2 Announce Type: replace-cross Abstract: Impulse-to-peak response (I2P) analysis for state-space ordinary differential equation (ODE) systems is a well-studied classical problem. However, the techniques employed for I2P optimal control of ODEs have not been extended to partial differential equation (PDE) systems due to the lack of a universal transfer function and state-space representation. Recently, however, partial integral equation (PIE) representation was proposed as...
$H_2$ optimal model reduction of linear systems with multiple quadratic outputs
Announce Type: replace Abstract: In this work, we consider the $H_2$ optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared $H_2$ system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the $H_2$ optimal approximation...
The myth of white Argentina still shapes the nation
The myth of white Argentina still shapes the nation Milei is carrying forward a state tradition that has long equated whiteness with progress. In late March, the United Nations General Assembly adopted a landmark resolution, spearheaded by Ghana and backed by the African Union and the Caribbean Community (CARICOM), recognising the transatlantic slave trade and chattel slavery as the gravest crime against humanity and calling for concrete steps towards reparations. A total of 123 member...
MetaboliSim: a Python implementation of the Mader model for dynamic and steady-state simulation of muscular energy metabolism
arXiv:2606.08366v1 Announce Type: cross Abstract: The Mader model is the most widely used mathematical framework for muscular energy metabolism in German-language sport science, underpinning lactate diagnostics, maximal lactate steady state (MLSS) estimation and training prescription. Despite decades of use, neither its dynamic ODE formulation nor its steady-state equations have been available as open code, leaving results based on the model impossible to reproduce independently. We close...
Auxiliary Gradient-Flow Solvers for Generalized Newtonian Models
Announce Type: new Abstract: We introduce an auxiliary gradient-flow framework for variational problems with generalized Newtonian structure governed by an N-function. The key idea is to replace the nonlinear constitutive dependence on the gradient, or symmetric gradient, by an auxiliary scalar variable representing its squared magnitude. This shifts the nonlinearity from the state equation to the auxiliary variable, yielding a sequence of uniformly elliptic weighted linear problems.
Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers
Announce Type: replace Abstract: Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks. These models rely on ODE/SDE solvers that integrate from a prior distribution to the data distribution; in many applications it is also highly desirable to integrate in the inverse direction. Standard solvers, however, accumulate discretization errors that prohibit exact inversion, an inaccuracy that is unacceptable in precision-critical...
Robust spectral preconditioning for high-P\'{e}clet number convection-diffusion
arXiv:2509.17531v2 Announce Type: replace Abstract: We introduce a two-level hybrid restricted additive Schwarz (RAS) preconditioner for heterogeneous steady-state convection-diffusion equations at high P\'{e}clet numbers. Our construction builds on the multiscale spectral generalized finite element method (MS-GFEM), wherein the coarse space is spanned by locally optimal basis functions obtained from local generalized eigenproblems on operator-harmonic spaces. Extending the theory of Ma...
HiPPO Zoo: Explicit Memory Mechanisms for Interpretable State Space Models
arXiv:2602.21340v2 Announce Type: replace Abstract: Representing the past in a compressed, efficient, and informative manner is a central problem for systems trained on sequential data. The HiPPO framework, originally proposed by Gu & Dao et al., provides a principled approach to sequential compression by projecting signals onto orthogonal polynomial (OP) bases via structured linear ordinary differential equations. Subsequent works have embedded these dynamics in state space models (SSMs),...
Second-order bulk-surface splitting for the wave equation with kinetic boundary conditions
Announce Type: new Abstract: This paper is devoted to the numerical analysis of a second-order bulk--surface splitting scheme for the semi-linear wave equation with kinetic boundary conditions. The construction is based on the interpretation of the equations as coupled system and the implementation of different difference formulae for the discrete states depending on their exact position in the system equations. This results in a 4-step scheme which decouples bulk and surface dynamics.