Molecular dynamics (MD) is a valuable tool for the investigation of functional elements in biomolecules, providing information on dynamic properties and processes. Previous work by our group has characterized static geometric properties of the two MHC α-helices comprising the peptide binding region recognized by T cells. We build upon this work and used several spline models to approximate the ...

The computation of the cumulative distribution (cdf), the complementary cdf (ccdf), and the density of certain shot-noise random variables is discussed. After subtracting oo a few terms that can be computed in closed form, what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a Fourier series whose coeecients are modulated samples of their ch...

Single-index models are important in multivariate nonparametric regression. In a previous paper, we proposed a penalized spline approach to a partially linear single-index model where the mean function has the form η0(α0 T x) +β0 T z. This approach is computationally stable and efficient in practice. Furthermore, it yields a root-n consistent estimate of the single-index parameter α and the par...

We consider polynomial spline spaces S r d (4) of degree d and smoothness r deened on triangulations. It is known that for d 3r + 2, S r d (4) possesses a basis of star-supported splines, i.e., splines whose supports are at most the set of triangles surrounding a vertex. Here we extend the theory by showing that for all d 3r + 1, there exist triangulations for which no such bases exist. 1. Intr...

in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. we derived the operational matrix of fractional integration of cubic and pantic b-spline scaling functions and used them to transform the mentioned equations to a ...

By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...

Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline   2 β t . In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline   2 β t Δ as an interpolation kernel. We verify ...