“DLMs augmented with polynomial-length chain-of-thought (CoT) can simulate any parallel sampling algorithm using an optimal number of sequential steps.”

“The paper proves that the chromatic number of $P_5$-free graphs is at most a polynomial function of the clique number.”

“The paper introduces computational deficiency ($δ_{\text{poly}}$) and the class LeCam-P (Decision-Robust Polynomial Time).”

“The eigenfunctions admit an expansion with universal coefficients so that the dependence on the twist $a$ is hidden only in these ground state eigenfunctions, and we suggest a general formula that allows one to construct these eigenfunctions from non-symmetric Macdonald polynomials.”

“Solutions are attracted toward the unique invariant probability measure at polynomial rates of arbitrary order.”

“Convolution defines a matrix transform that preserves positivity.”

“The paper introduces two complementary high-order strategies for triangular elements: a reduced quadrilateralization approach and a triangle based spectral element method based on Dubiner polynomials.”

“The paper derives the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim.”

“The paper proves that the unreduced singular instanton homology has 2-torsion for any null-homologous fibered knot (except for a specific case) and provides a formula for calculating it.”

“The modular reduction allows us to exploit any SLC sampling algorithm in order to traverse the backwards path, and we establish novel guarantees with short proofs for both uni-modal and multi-modal densities.”

“The paper proposes two original algorithms: a generic polynomial-time sequential algorithm with theoretical guarantees and an extension of the General Yankee Swap.”

“The paper establishes general criteria that guarantee equivalences between the categories of polynomial functors of different degrees or with different base categories.”

“All models are exactly-solvable, admit algebraic forms for the Hamiltonian and integrals, have polynomial eigenfunctions, hidden algebraic structure, and possess a polynomial algebra of integrals.”

“The paper derives an exact semidefinite characterization of nonnegative APS and introduces a derivative-based regularizer that promotes smoothly varying APS profiles while preserving transitions of clusters.”

“The findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.”

“The paper provides explicit code parameters and properties as well as some additional bounds on parameters such as rank and distance.”

“The proposed preconditioners significantly accelerate the convergence of iterative solvers compared to existing methods.”

“The paper's core finding is that every circuit-level Pauli error in these protocols propagates to a Clifford error at the end, enabling efficient simulation.”

“The paper presents polynomial-time algorithms for MSC in several nontrivial settings.”

“The paper finds that as the modification parameter increases, neutron stars grow in both radius and mass, and a 'frozen state' emerges, forming a critical horizon.”

“Propositional logics are usually polynomial-time reducible to their fragments with at most two variables (often to the one-variable or even variable-free fragments).”

“The paper classifies the centrality and commutativity of skew-polynomial algebras depending on the Lie type and the order of the root of unity.”

“The paper utilizes a sampling-free intrusive stochastic Galerkin approach and domain decomposition (DD)-based solvers.”

“The error of approximation of the $2π$-periodic sawtooth function $(π-x)/2$, $0\leq x<2π$, by its $n$-th Fourier polynomial is shown to be bounded by arccot$((2n+1)\sin(x/2))$.”

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“The paper proves that $K_0(X_{n,k})$ is canonically isomorphic to $R_{n,k}$, extending classical isomorphisms for the flag variety.”

“The paper provides the first general framework for attaining statistically near-optimal performance under broad geometric constraints while preserving computational tractability.”

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“The paper derives moderate deviation estimates for the height function in both the upper and lower tail regimes, with sharp exponents and constants.”

“The article's subject matter is the theoretical underpinnings of pre-Hilbert structures on polynomial spaces and their associated Laplacians.”

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“The paper completely characterizes a class of permutation polynomials of the form $L(X)+γTr_q^{q^3}(c_1X+c_2X^2+c_3X^3+c_4X^{q+2})$ over $\mathbb{F}_{q^3}$.”

“The paper proves that $χ\leq f(ω),$ where $f$ is a polynomial of degree $2j-2i-4.$”

“The paper establishes a near-optimal structural characterization of the vectors w and v under the assumption that the concentration probability is polynomially large. It also shows that if both w and v have distinct entries, then sup_x P(S_π=x) ≤ n^{-5/2+o(1)}.”

“Sparse relaxations recover coalition structures whose welfare is arbitrarily close to optimal in polynomial time with high probability.”

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“The article's focus is on the 'Categorification of Chromatic, Dichromatic and Penrose Polynomials.'”

“Our main result is the significantly improved sample complexity for learning such low-degree polynomials.”

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“The paper studies shallow neural networks' ability to learn low-degree spherical polynomials.”

“The article uses the Jones polynomial to prove infinite families of knots satisfy the Cosmetic Surgery Conjecture.”

“The article's focus is on the polynomial numerical index with respect to a norm-one polynomial.”

“The paper focuses on the Degenerate Euler-Seidel Method.”

“The article likely explores the evolution of polynomial zeroes under the influence of the heat equation.”

“The article's content is likely highly technical and aimed at a specialized audience.”

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“The research focuses on Physics-informed Polynomial Chaos Expansion with Enhanced Constrained Optimization Solver and D-optimal Sampling.”

“The article's abstract would provide more specific details on the methodology and results.”

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