
Sharp Effective FiniteField Nullstellensatz
The (weak) Nullstellensatz over finite fields says that if P_1,…,P_m are...
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The sumofsquares hierarchy on the sphere, and applications in quantum information theory
We consider the problem of maximizing a homogeneous polynomial on the un...
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Sparse Polynomial Interpolation Based on Diversification
We consider the problem of interpolating a sparse multivariate polynomia...
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Planar Polynomials arising from Linearized polynomials
In this paper we construct planar polynomials of the type f_A,B(x)=x(x^q...
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Log orthogonal functions: approximation properties and applications
We present two new classes of orthogonal functions, log orthogonal funct...
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Temperature expressions and ergodicity of the NoséHoover deterministic schemes
Thermostats are dynamic equations used to model thermodynamic variables ...
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Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers
This paper presents a unified approach to the modeling and computation o...
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Modified discrete Laguerre polynomials for efficient computation of exponentially bounded Matsubara sums
We develop a new type of orthogonal polynomial, the modified discrete Laguerre (MDL) polynomials, designed to accelerate the computation of bosonic Matsubara sums in statistical physics. The MDL polynomials lead to a rapidly convergent Gaussian "quadrature" scheme for Matsubara sums, and more generally for any sum F(0)/2 + F(h) + F(2h) + ⋯ of exponentially decaying summands F(nh) = f(nh)e^nhs where hs>0. We demonstrate this technique for computation of finitetemperature Casimir forces arising from quantum field theory, where evaluation of the summand F requires expensive electromagnetic simulations. A key advantage of our scheme, compared to previous methods, is that the convergence rate is nearly independent of the spacing h (proportional to the thermodynamic temperature). We also prove convergence for any polynomially decaying F.
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