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Entropies, cross-entropies and Rényi divergence: sharp three-term inequalities for probability density functions

This paper establishes a new sharp three-term inequality linking differential Rényi entropy, Rényi divergence, and Rényi cross-entropy for probability density functions, demonstrating that equality holds when one density is an escort of the other and using this result to derive further sharp bounds involving various informational functionals like absolute moments and Fisher information.

Razvan Gabriel Iagar, David Puertas-Centeno2026-03-10🔢 math

Aero-Promptness: Drag-Aware Aerodynamic Manipulability for Propeller-driven Vehicles

This paper introduces Drag-Aware Aerodynamic Manipulability (DAAM), a geometric framework for control allocation in redundant multirotors that utilizes a Riemannian metric to explicitly account for motor torque limits and aerodynamic drag, thereby generating a state-dependent manipulability volume that serves as a natural barrier function to optimize redundancy resolution while characterizing the resulting smooth manifolds and global jump discontinuities.

Antonio Franchi2026-03-10🔢 math

Post-Hoc Large-Sample Statistical Inference

This paper develops a theory of asymptotic post-hoc inference that utilizes e-values to create sharper confidence sets and p-values with weaker assumptions than existing nonasymptotic methods, thereby allowing valid statistical conclusions even when significance levels are chosen after observing the data.

Ben Chugg, Etienne Gauthier, Michael I. Jordan, Aaditya Ramdas, Ian Waudby-Smith2026-03-10🔢 math

Primitive recursive categoricity spectra

This paper investigates the primitive recursive analogue of computable categoricity spectra, demonstrating that these notions coincide for several natural classes of structures, including relatively $\Delta_{2}^{0}$ -categorical equivalence structures and linear orders, relatively $\Delta_{3}^{0}$ -categorical Boolean algebras, and computably categorical trees as partial orders.

Nikolay Bazhenov, Heer Tern Koh, Keng Meng Ng2026-03-10🔢 math

Primitive recursive categoricity spectra of functional structures

This paper investigates the relationship between degrees of categoricity and their punctual (primitive recursive) analogues for functional structures, demonstrating that these notions coincide for non- $\Delta_{1}^{0}$ -categorical injection structures but diverge for certain $\Delta_{1}^{0}$ -categorical ones, while also establishing the existence of specific PR-degrees with distinct properties in every non-zero c.e. Turing degree.

Nikolay Bazhenov, Heer Tern Koh, Keng Meng Ng2026-03-10🔢 math

On Representing Matroids via Modular Independence

This paper introduces a matrix-based notion of matroid representation over local commutative rings using modular independence, establishing conditions under which this system forms a matroid, deriving structural properties for codes over chain rings, and demonstrating that certain non-field-representable matroids, such as the Vámos matroid, can be represented over rings like $\mathbb{Z}/8\mathbb{Z}$ .

Koji Imamura, Keisuke Shiromoto2026-03-10🔢 math

Higher operad structure for Fukaya categories

This paper establishes a natural $\mathbf{fc}$ -multicategory structure on moduli spaces of pseudo-holomorphic polygons to provide a uniform operadic framework for various $A_\infty$ -type structures, including Fukaya categories, as algebras over differential graded $\mathbf{fc}$ -multicategories.

Hang Yuan2026-03-10🔢 math

A generalization of Kadell's orthogonality ex-conjecture

This paper generalizes Zhou's 2021 recursion for a specific constant term identity—originally conjectured by Kadell and later proved by Károlyi, Lascoux, and Warnaar—by categorizing the variables into two parts to extend the result to a broader context.

Zihao Huang, Wenlong Jiang, Yue Zhou2026-03-10🔢 math

Asymptotic Analysis of Discrete-Time Hawkes Process

This paper investigates the discrete-time Hawkes process by establishing its Large Deviation Principle, analyzing the limiting behavior of the associated arrival process, and demonstrating its application in modeling insurance claims.

Utpal Jyoti Deba Sarma, Dharmaraja Selvamuthu2026-03-10🔢 math

Finite-Horizon Optimal Consumption and Investment with Time-Varying Job-Switching Costs

This paper characterizes an agent's optimal consumption, investment, and time-varying job-switching strategies over a finite horizon by reducing the dual problem to a parabolic double obstacle problem with time-dependent obstacles, for which existence, uniqueness, and free boundary smoothness are rigorously established using PDE theory.

Gugyum Ha, Junkee Jeon, Jihoon Ok2026-03-10🔢 math

Coupling-Aware RHS Beamforming for Wideband Multi-User Sum Rate Maximization

This paper proposes a coupling-aware wideband reconfigurable holographic surface (RHS) model and a Jacobian-aided WMMSE-based joint beamforming framework to maximize multi-user sum rate by effectively mitigating mutual coupling effects while satisfying practical power constraints, with its validity confirmed through Meep simulations and numerical experiments.

Liangshun Wu, Wen Chen2026-03-10🔢 math

Patrolling cop vs omniscient robber

This paper introduces and systematically analyzes a variant of the Cops and Robbers game where a cop follows a predetermined patrol against an omniscient robber, determining the minimum capture radius required for various graph classes including trees, grids, and chordal graphs.

Nina Chiarelli, Paul Dorbec, Miloš Stojakovic, Andrej Taranenko2026-03-10🔢 math

Serre conjecture II for pseudo-reductive groups

This paper generalizes Serre conjecture II to pseudo-reductive groups by proving its equivalence to the original conjecture for semisimple groups, thereby establishing that every torsor under a pseudo-semisimple, simply connected group over global function fields or non-archimedean local fields possesses a rational point.

Mac Nam Trung Nguyen2026-03-10🔢 math

Asymptotic normality for general subtree counts in conditioned Galton--Watson trees

This paper proves that, under a mild moment condition, the number of occurrences of a fixed rooted plane tree as a general subtree in a conditioned Galton--Watson tree is asymptotically normal with linear mean and variance, thereby confirming a conjecture by Janson and demonstrating that the result fails if the moment condition is violated.

Fameno Rakotoniaina, Dimbinaina Ralaivaosaona2026-03-10🔢 math

On embeddings of homogeneous quandles

This paper establishes a necessary and sufficient condition for embedding homogeneous quandles associated with a triplet $(G,H,\sigma)$ into conjugation quandles, thereby generalizing existing results for Alexander quandles and providing new insights into core, Grassmann, and rotation quandles.

Ayu Suzuki2026-03-10🔢 math

Stability of Two-Stage Stochastic Programs Under Problem-Dependent Costs

This paper establishes a direct primal-based stability framework for two-stage stochastic programs with problem-dependent costs, proving Lipschitz continuity of the optimal value function under a regret domination property and demonstrating its applicability to both continuous and mixed-integer second-stage problems.

Nils Peyrousset, Benoît Tran2026-03-10🔢 math

Introduction to non-Abelian Patchworking

This paper introduces the framework of non-Abelian patchworking, a geometric method for constructing real algebraic surfaces in $\mathbb{R}P^3$ via the real locus of non-Abelian complex-phase tropical hypersurfaces, which successfully reproduces all isotopy types of surfaces up to degree three and reveals that primitive $PGL_2$ surfaces can exhibit Euler characteristics distinct from their complex counterparts.

Turgay Akyar, Mikhail Shkolnikov2026-03-10🔢 math

An Equivalent form of Twin Prime Conjecture connected with a sequence of arithmetic progressions

This paper proposes an equivalent formulation of the Twin Prime Conjecture based on a symmetric property observed within a specific sequence of arithmetic progressions defined for pairs of coprime integers.

Srikanth Cherukupally2026-03-10🔢 math

Topological insights into Monoids and Module systems

This paper generalizes several topological results and concepts from ring theory to the setting of monoids.

Doniyor Yazdonov, Carmelo Antonio Finocchiaro2026-03-10🔢 math

A Semi-Discrete Optimal Transport Scheme for the Semi-Geostrophic Slice Compressible Model

This paper introduces and validates a novel semi-discrete optimal transport scheme for the compressible semi-geostrophic slice model that utilizes $c$ -exponential charts to efficiently construct $c$ -Laguerre tessellations, thereby enabling mass- and energy-conserving simulations of large-scale atmospheric dynamics while preserving key geometric structures.

Théo Lavier, Beatrice Pelloni2026-03-10🔢 math

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