This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…

This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

The paper analyzes the phase transitions of the noisy transformer model on the unit sphere, proving a sharp global-minimizer dichotomy that depends on the dimension and coupling strength.

This paper characterizes the graph structure, including cycle and path lengths, of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, demonstrating strong regularities desp…

This paper establishes an exact mathematical correspondence between training and inference in deep learning and the solution of Hamilton-Jacobi partial differential equations, unifying multiple theore…

The paper proposes a novel hybrid framework that couples Large Language Models (LLMs) with simplified physics-based simulations to improve the synthesis planning of novel inorganic crystalline materia…

The paper introduces a computational framework using Hodge zero-modes to track the geometry of topological features in parameter-dependent data, providing metrics like curvature and holonomy to quanti…

The paper proves that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations.

This paper presents an algorithmic framework for exhaustively generating and tabulating knot and link diagrams on the thickened torus.

The paper introduces Strong Stochastic Flow Maps (SSFMs), a novel framework that directly learns the strong solution map of additive-noise Stochastic Differential Equations (SDEs), enabling few-step s…

The paper introduces and explores Truly Linear FPT (TLFPT), a complexity class defined by $O(n) + f(k)$, demonstrating that it is a strict subset of standard Linear FPT and providing new algorithms fo…

The paper introduces the $\alpha$-Wasserstein mechanism to achieve Rényi Pufferfish Privacy using Laplace and Gaussian noise, demonstrating that it generalizes existing privacy frameworks and reduces…

The paper develops a quantitative framework to analyze and improve flow distillation in diffusion models, providing stability guarantees and suggesting non-uniform time scheduling to reduce approximat…

This paper proves several properties about Extended Frege proof systems and circuit equivalence.

The paper introduces AutoformBot, a multi-agent system that successfully autoformalizes a large corpus of open-access graduate-level mathematics textbooks into a verified library in Lean 4, demonstrat…

The paper introduces a method to efficiently detect 'essential' constraints in Boolean MinCSPs, significantly reducing the search space for solving these problems and providing a dichotomy theorem for…

The paper models latent worker preferences in gig labor markets using the Preisach hysteresis model, demonstrating that predicting acceptance rates can simultaneously reduce labor costs and increase s…

This paper determines that verifying global parameter identifiability for linear ODE models is an NP-hard problem, establishing a computational complexity boundary for the field.

The paper empirically and theoretically demonstrates that incorporating Lamarckian and Baldwinian mechanisms into evolutionary algorithms significantly outperforms standard Darwinian evolution, especi…