We describe the development of a scoring function designed to model the hydrophobic effect in protein folding. An optimization technique is used to determine the best functional form of the hydrophobic potential. The scoring function is expanded using the Chebyshev polynomials, for which the coefficients are determined by minimizing the Z-score of native structures in the ensembles of alternate...

When a function f(x) is holomorphic on an interval x ∈ [a, b], its roots on the interval can be computed by the following three-step procedure. First, approximate f(x) on [a, b] by a polynomial fN (x) using adaptive Chebyshev interpolation. Second, form the Chebyshev– Frobenius companion matrix whose elements are trivial functions of the Chebyshev coefficients of the interpolant fN (x). Third, ...

Calculating the spectral function of two dimensional systems is arguably one most pressing challenges in modern computational condensed matter physics. While efficient techniques are available lower dimensions, present insurmountable hurdles, ranging from sign problem quantum Monte Carlo (MC), to entanglement area law tensor network based methods. We hereby a variational approach on Chebyshev e...