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The State-Dependent Riccati Equation in Nonlinear Optimal Control: Analysis, Error Estimation and Numerical Approximation

This paper analyzes the theoretical foundations, error bounds, and numerical approximations of the State-Dependent Riccati Equation (SDRE) approach for nonlinear optimal control, introducing a residual-minimizing decomposition strategy and demonstrating through numerical experiments that the Newton-Kleinman iterative method offers superior stability and cost-effectiveness compared to the offline-online approach.

Luca SaluzziTue, 10 Ma🔢 math

Scenario Reduction for Distributionally Robust Optimization

This paper introduces a general scenario reduction method for distributionally robust optimization that projects the original ambiguity set onto a reduced set of scenarios, providing theoretical quality bounds and demonstrating significant computational efficiency with minimal loss in solution accuracy across discrete and continuous distributions.

Kevin-Martin Aigner, Sebastian Denzler, Frauke Liers, Sebastian Pokutta, Kartikey SharmaTue, 10 Ma🔢 math

On the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds

This paper introduces the $\mathcal{D}^+_J$ operator on higher-dimensional almost Kähler manifolds to investigate the $\bar{\partial}$ -problem and establish uniqueness and local existence results for a generalized Monge-Ampère equation, ultimately providing an elliptic system for the operator and reorganizing the work of Tosatti-Weinkove-Yau.

Qiang Tan, Hongyu Wang, Ken Wang, Zuyi ZhangTue, 10 Ma🔢 math

On Supports for graphs of bounded genus

This paper establishes that for hypergraphs derived from cross-free connected subgraphs of a bounded-genus host graph, there exists a support graph that also maintains bounded genus, thereby generalizing prior planar results and providing a unified framework for solving packing, covering, and coloring problems on surfaces.

Rajiv Raman, Karamjeet SinghTue, 10 Ma🔢 math

Computing adjoint mismatch of linear maps

This paper proposes and analyzes a stochastic algorithm that provably converges almost surely to the operator norm of the difference between two linear maps—one accessible only via forward evaluation and the other only via adjoint evaluation—by performing a random search on a generalized Rayleigh quotient with optimal step sizes.

Jonas Bresch, Dirk A. Lorenz, Felix Schneppe, Maximilian WinklerTue, 10 Ma🔢 math

Big Ramsey degrees and the two-branching pseudotree

This paper establishes that finite chains within the two-branching countable ultrahomogeneous pseudotree possess finite big Ramsey degrees, specifically determining the degree for chains of length two to be seven, thereby presenting the first example of a countable ultrahomogeneous structure in a finite language where some finite substructures have finite big Ramsey degrees while others have infinite ones.

David Chodounský, Natasha Dobrinen, Thilo WeinertTue, 10 Ma🔢 math

The holonomy Lie $\infty$ -groupoid of a singular foliation I

This paper constructs a finite-dimensional Kan simplicial manifold that integrates the universal Lie $\infty$ -algebroid of a singular foliation admitting a geometric resolution, utilizing a recursive application of bi-submersions to generalize the Androulidakis-Skandalis holonomy groupoid to a higher Lie groupoid setting.

Camille Laurent-Gengoux (IECL), Ruben Louis (UIUC)Tue, 10 Ma🔢 math

Algorithmic randomness and the weak merging of computable probability measures

This paper characterizes Martin-Löf and Schnorr randomness by establishing that these notions correspond to the weak merging of computable probability measures under the summable Kullback-Leibler divergence, a result derived by linking the divergence to the incremental growth of the Doob decomposition of a specific submartingale.

Simon M. Huttegger, Sean Walsh, Francesca Zaffora BlandoTue, 10 Ma🔢 math

Construction and classification of differential symmetry breaking operators for principal series representations of the pair $(SO_0(4,1), SO_0(3,1))$ for special parameters

This paper constructs and provides a complete classification of all differential symmetry breaking operators between specific vector and line bundles over the 3-sphere and 2-sphere, respectively, in the special case where the rank parameter $N$ equals the absolute value of the integer $m$ .

Víctor Pérez-ValdésTue, 10 Ma🔢 math

On the torsion growth in quadratic number fields for elliptic curves defined over the rationals

This paper investigates the inverse problem of determining the properties of a quadratic number field based on the growth of an elliptic curve's torsion subgroup defined over the rationals, establishing an explicit relationship between the primes dividing the curve's conductor and the conductor of the field extension.

Sara Arias-de-Reyna, Miguel Pineda-Martín, José M. TorneroTue, 10 Ma🔢 math

Robustness of topological phases on aperiodic lattices

This paper investigates the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms between groupoid and coarse-geometric models, demonstrating that strong phases are detected by position spectral triples while phases arising from stacking along Delone sets are inherently weak in the coarse-geometric sense.

Yuezhao LiTue, 10 Ma🔢 math

Strong order 1 adaptive approximation of jump-diffusion SDEs with discontinuous drift

This paper introduces a novel transformation-based, doubly-adaptive quasi-Milstein scheme for jump-diffusion SDEs with discontinuous drift and degenerate diffusion, achieving a strong convergence rate of order 1 in $L^p$ under assumptions weaker than those in existing literature.

Verena SchwarzTue, 10 Ma🔢 math

WG-IDENT: Weak Group Identification of PDEs with Varying Coefficients

This paper introduces WG-IDENT, a robust framework that combines weak formulations, B-spline representations with spectrally optimized knots, and a novel group feature trimming technique to accurately identify Partial Differential Equations with spatially varying coefficients from heavily noisy spatiotemporal data.

Cheng Tang, Roy Y. He, Hao LiuTue, 10 Ma🔢 math

An Operator Splitting Method for Large-Scale CVaR-Constrained Quadratic Programs

This paper introduces CVQP, an open-source operator splitting method that efficiently solves large-scale quadratic programs with Conditional Value-at-Risk (CVaR) constraints by combining a specialized $O(m\log m)$ projection algorithm with parallel computations, achieving performance orders of magnitude faster than general-purpose solvers for problems involving millions of scenarios.

Eric Luxenberg, David Pérez-Piñeiro, Steven Diamond, Stephen BoydTue, 10 Ma🔢 math

Quantitative Convergence for Sparse Ergodic Averages in $L^1$

This paper establishes a unified framework for proving the almost everywhere pointwise convergence of sparse ergodic averages in $L^1$ for both deterministic and random sequences within specific parameter ranges, while providing new quantitative convergence estimates that improve upon previous non-quantitative results.

Ben Krause, Yu-Chen SunTue, 10 Ma🔢 math

A general approach to distributed operator splitting

This paper introduces a general forward-backward splitting framework utilizing coefficient matrices to solve monotone inclusion problems with non-cocoercive operators, unifying existing algorithms while enabling new flexible and distributed implementations.

Minh N. Dao, Matthew K. Tam, Thang D. TruongTue, 10 Ma🔢 math

Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions

This paper introduces an adaptive replication strategy within a trust-region Bayesian optimization framework that dynamically allocates repeated evaluations to effectively manage high-variance stochastic functions, significantly improving both solution accuracy and computational efficiency compared to baseline methods.

Mickael Binois (ACUMES), Jeffrey Larson (ANL)Tue, 10 Ma🔢 math

The monodromy of compact Lagrangian fibrations

This paper investigates the monodromy representations of compact Lagrangian fibrations, proving their irreducibility over $\mathbb{C}$ when the period map is generically immersive and characterizing the structure of these representations as a direct sum of two irreducible local systems in the isotrivial case.

Edward VarvakTue, 10 Ma🔢 math

Martingale problem of the two-dimensional stochastic heat equation at criticality

This paper establishes an exact recursive equation for the covariation measures of the two-dimensional stochastic heat equation at criticality, explicitly expressing the quadratic variations of its martingale parts in terms of the equation's solutions and two-body delta-Bose gas semigroups through asymptotic analysis and new fourth-order moment bounds.

Yu-Ting ChenTue, 10 Ma🔢 math

Hypergraph Characterization of Fusion Rings

This paper establishes a correspondence between multiplicity-free, self-dual fusion rings and digraph-hypergraph pairs to characterize these rings via graphical properties and to classify all non-isomorphic instances of rank at most 8.

Paul Bruillard, Kathleen Nowak, Stephen J. YoungTue, 10 Ma🔢 math

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