math papers | Gist.Science

Iterated club shooting and the stationary-logic constructible model

This paper investigates the iteration of the stationary-logic constructible model $C(\mathtt{aa})$ by proving distributivity and stationary-set preservation for countable iterations of club-shooting forcings using mutually stationary sets, and introducing mutually fat sets to achieve stronger results for uncountable iterations, thereby demonstrating the ability to force models where $V=C(\mathtt{aa})$ and where iterated $C(\mathtt{aa})$ sequences decrease with arbitrarily large order types.

Ur Ya'ar2026-03-10🔢 math

Circularity of Thermodynamical Material Networks: Indicators, Examples, and Algorithms

This paper introduces a graph-based framework for Thermodynamical Material Networks (TMNs) that models circular economy material flows using dynamic energy and mass balances, proposes new circularity indicators, and validates the approach through numerical simulations of fluid and solid material systems.

Federico Zocco2026-03-10🔢 math

On the elliptical range theorems for the Davis-Wielandt shell, the numerical range, and the conformal range

This paper presents various elementary approaches to elliptical range theorems for the Davis-Wielandt shell, numerical range, and conformal range, focusing on their quadratic representations.

Gyula Lakos2026-03-10🔢 math

Amenable equivalence relations, Kesten's property, and measurable lamplighters

This paper characterizes the amenability of countable Borel equivalence relations via the uniform Liouville property, investigates Kesten's property for return probabilities on topological groups, and constructs an amenable contractible Polish group lacking this property by linking it to anti-concentration inequalities in measurable lamplighter groups.

Maksym Chaudkhari, Kate Juschenko, Friedrich Martin Schneider2026-03-10🔢 math

Bilevel Optimization and Heuristic Algorithms for Integrating Latent Demand into the Design of Large-Scale Transit Systems

This paper introduces a bilevel optimization model (TN-DA) for designing large-scale transit networks that integrates latent demand through rider adoption behavior, and proposes five efficient heuristic algorithms that outperform exact methods in computational speed while maintaining high solution quality and key adoption properties in real-world case studies.

Hongzhao Guan, Beste Basciftci, Pascal Van Hentenryck2026-03-10🔢 math

Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functional

This paper demonstrates that by strategically combining sample splitting with specific nuisance function tuning strategies (such as undersmoothing or oversmoothing), both plug-in and first-order bias-corrected estimators can achieve minimax rates of convergence for doubly robust functionals across all Hölder smoothness classes, overcoming limitations of existing literature.

Sean McGrath, Rajarshi Mukherjee2026-03-10🔢 math

Erratum and original of Port-Hamiltonian structure of interacting particle systems and its mean-field limit

This paper presents a minimal port-Hamiltonian formulation for interacting particle systems to analyze their stability and mean-field limits, while simultaneously issuing an erratum that corrects a previous claim regarding trajectory compactness by providing a counterexample for repulsive interactions and a revised proof for Hamiltonian gradient convergence.

Jannik Daun, Daniel Jannik Happ, Birgit Jacob, Claudia Totzeck2026-03-10🔢 math

Geodesic slice sampling on the sphere

This paper introduces efficient, parameter-free geodesic slice sampling algorithms for generating samples from probability distributions on the sphere, proving their uniform ergodicity and demonstrating superior performance over standard methods like random-walk Metropolis-Hastings and Hamiltonian Monte Carlo in challenging directional data scenarios.

Michael Habeck, Mareike Hasenpflug, Shantanu Kodgirwar, Daniel Rudolf2026-03-10🔢 math

Hodge-Newton indecomposability and a combinatorial identity

This paper introduces a simplified perspective on Hodge-Newton indecomposability to provide a uniform proof of a combinatorial identity derived from affine Deligne-Lusztig varieties with finite Coxeter parts.

Dong Gyu Lim2026-03-10🔢 math

Fixed-domain curve counts for blow-ups of projective space

This paper investigates the asymptotic agreement and divergence between geometric and virtual counts of pointed curves with fixed complex structure in blow-ups of projective space, providing explicit formulas for toric cases via Jacobian integrals and computing virtual counts for $\text{Bl}_q(\mathbb{P}^r)$ using quantum cohomology.

Alessio Cela, Carl Lian2026-03-10🔢 math

Small mass limit of expected signature for physical Brownian motion

This paper establishes the convergence of the expected signature of a generalized physical Brownian motion to a nontrivial tensor in the small mass limit ( $m \to 0^+$ ) by analyzing a graded PDE system, revealing that the limit differs from the standard mathematical Brownian motion and exhibits explicit combinatorial patterns when the system's coefficient matrix is diagonalizable.

Siran Li, Hao Ni, Qianyu Zhu2026-03-10🔢 math

Integral cohomology rings of weighted Grassmann orbifolds and rigidity properties

This paper introduces weighted Grassmann orbifolds via Plücker weight vectors, classifies them up to homeomorphism, establishes conditions for torsion-free integral cohomology, and explicitly computes their integral cohomology rings and equivariant structure constants.

Koushik Brahma2026-03-10🔢 math

Home Energy Management under Tiered Peak Power Charges

This paper proposes a model predictive control policy for home battery management under tiered peak power charges that, using simple forecasts, achieves electricity costs within 1.7% of the theoretical minimum derived from perfect foresight.

David Pérez-Piñeiro, Sigurd Skogestad, Stephen Boyd2026-03-10🔢 math

On colorings of hypergraphs embeddable in $\mathbb{R}^d$

This paper improves upon previous results by Heise et al. by proving that the weak chromatic number of $k$ -uniform hypergraphs arising from linearly or PL-embeddable simplicial complexes in $\mathbb{R}^d$ is infinite for most dimensions and uniformities, and further extends these findings to show that the weak chromatic number of $s$ -dimensional faces in triangulations of any fixed triangulable $d$ -manifold is infinite for all $1 \le s \le d$.

Seunghun Lee, Eran Nevo2026-03-10🔢 math

The Legendre transform, the Laplace transform and valuations

This paper characterizes the Legendre, Laplace, and identity transforms as the unique continuous, $\mathrm{SL}(n)$ contravariant valuations with specific conjugation or duality properties on spaces of convex and log-concave functions.

Jin Li2026-03-10🔢 math

The inverse problem of convex polygon coordinates

This paper focuses on convex polygons in the plane by summarizing and comparing Gibbs coordinates (based on entropy maximization and exponential functions) with Wachspress coordinates (rational functions), identifying their points of agreement and divergence, and demonstrating how Gibbs coordinates for polygons with rational vertices can be interpreted as algebraic functions.

A. B. Romanowska, J. D. H. Smith, A. Zamojska-Dzienio2026-03-10🔢 math

On the rook polynomial of grid polyominoes

This paper establishes that the rook polynomial of grid polyominoes coincides with the h-polynomial of their corresponding coordinate rings by utilizing simplicial complex theory to generalize previous findings on frame polyominoes.

Rodica Dinu, Francesco Navarra2026-03-10🔢 math

Integral equation methods for acoustic scattering by fractals

This paper establishes a well-posed first-kind integral equation formulation for acoustic scattering by general compact scatterers, including fractals, and develops a convergent piecewise-constant Galerkin discretization with proven rates for fractal attractors, supported by a fully discrete implementation and numerical examples in Julia.

A. M. Caetano, S. N. Chandler-Wilde, X. Claeys + 3 more2026-03-10🔢 math

On the Ziv-Merhav theorem beyond Markovianity

This paper extends the Ziv-Merhav theorem on universal estimation of specific cross-entropy from multi-level Markov measures to a broader class of decoupled measures, including regular g-measures and equilibrium measures from statistical mechanics.

Nicholas Barnfield, Raphaël Grondin, Gaia Pozzoli + 1 more2026-03-10🔢 math

The Martingale Sinkhorn Algorithm

This paper introduces and proves the convergence of a Martingale Sinkhorn algorithm in arbitrary dimensions for solving the martingale Benamou–Brenier optimal transport problem, extending the theory to marginals with finite moments of order $p > 1$ without requiring compact support.

Manuel Hasenbichler, Benjamin Joseph, Gregoire Loeper, Jan Obloj, Gudmund Pammer2026-03-10🔢 math

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