Accelerated molecular dynamics (aMD) simulations greatly improve the efficiency of conventional molecular dynamics (cMD) for sampling biomolecular conformations, but they require proper reweighting for free energy calculation. In this work, we systematically compare the accuracy of different reweighting algorithms including the exponential average, Maclaurin series, and cumulant expansion on th...

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.

In this article, we introduce and study a new family P?(?,?,k,?,?,?,r) of normalized analytic ?-pseudo-starlike bi-univalent functions by using the Horadam polynomials, which is associated with certain convolution operator defined in open unit disk U. We establish bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Furthermore, obtain Fekete-Szeg? inequality class P? (...

In Exact Real Arithmetic, real numbers are represented as potentially infinite streams of information units, called digits. In this paper, we work in the framework of Linear Fractional Transformations (LFT’s, also known as Möbius transformations) that provide an elegant approach to real number arithmetic (Gosper 1972, Vuillemin 1990, Nielsen and Kornerup 1995, Potts and Edalat 1996, Edalat and ...

Much research has been performed on the efficient design and implementation of finite impulse response (FIR) digital differentiators. Some of the commonly used design procedures include windows based designs [1], minimax designs [2], eigenfilters [3], [4], optimization techniques [5], the weighted least squares technique [6], and a recent design with optimal noise attenuation [7]. Another impor...

A new type of Taylor series based 2-D finite difference approximation is presented, and it is shown that the coefficients of these approximations are not unique. Explicit formulas are presented for one of the possible sets of coefficients for an arbitrary order, by extending the previously presented 1-D approximations. These coefficients are implemented as maximally linear 2-D FIR digital diffe...

We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of Rn × R.

We study a special type of infinite product, called an infinite product of Cardano type, and we obtain its Taylor series. We prove that Hadamard's factorization of bandlimited signals is given by an infinite product of Cardano type, and apply our results to obtain the Taylor series for bandlimited signals.

Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of n variables by fixing a direction in Rn. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariat...

The nonlinear filters based on Taylor series approximation are broadly used for computational simplicity, even though their filtering estimates are clearly biased. In this paper, first, we analyze what is approximated when we apply the expanded nonlinear functions to the standard linear recursive Kalman filter algorithm. Next, since the state variables αt and αt−1 are approximated as a conditio...