Second-order Spline Research Articles

PEMODELAN REGRESI NONPARAMETRIK DENGAN ESTIMATOR SPLINE POLYNOMIAL TRUNCATED PADA DATA JUMLAH WISATAWAN NUSANTARA

The nonparametric regression approach is a statistical method used to determine the relationship between predictor variables and the dependent variable when the assumed pattern is unknown. Truncated spline is an estimator used in nonparametric regression to handle data with varying behaviors. Nonparametric regression modeling with truncated polynomial spline was applied to local Indonesian tourist visitation data obtained from BPS for the years 2017-2019, for each month. The optimal knot points were selected based on the smallest Gross Cross Validation values. Based on the analysis, the optimal model is a second-order spline with the smallest Gross Cross Validation value of 17,95 and the optimal knot points are in the 2nd, 6th, and 7th months. The goodness of the model is evident from an value of 81,88% and an MSE of 12,46. The best model obtained shows a fairly accurate ability to explain the estimated number of domestic tourists so that it can be a basis for stakeholders to make key decisions in planning and managing the tourism industry as an effort to increase domestic tourism interest.

Local Elevation Umbrella Sampling Applied to the Calculation of Alchemical Free-Energy Changes via λ-Dynamics: The λ-LEUS Scheme

When using molecular dynamics (MD) simulations for the calculation of alchemical free-energy changes, the extended-dynamics method called λ-dynamics (λD) in its currently available implementations does not compare very favorably with thermodynamic integration (TI) in terms of robustness, efficiency, and accuracy, although it is in principle easier to set up, postprocess, and automatize. In the present article, the main shortcomings of the λD approach are carefully analyzed, and possible remedies are proposed. The resulting scheme, called λ-LEUS, involves: (i) the use of a simple noninvertible coordinate transformation ensuring a finite sampling of the two physical end states; (ii) the application of the local elevation umbrella sampling (LEUS) memory-based biasing scheme to enforce homogeneous sampling and overcome barriers along the alchemical coordinate; (iii) recommendations concerning the choice of the mass parameter and of the temperature-coupling scheme for this coordinate; (iv) the use of a second-order splines basis set for the memory-based biasing functions. The λ-LEUS scheme is described and tested considering the perturbation of hydroquinone to benzene in water. The results are compared to those of TI calculations and exhibit a superior accuracy-to-efficiency ratio, presumably because dynamic variations in the alchemical coordinate open up pathways to circumvent orthogonal barriers, these pathways being inaccessible when the coordinate is constrained. Therefore, λ-LEUS combines the practical advantages of λD with the robustness of TI, simultaneously affording a slightly enhanced computational efficiency.

Image and Complex Correlation Near Discontinuities

Abstract: In this paper, the effect of imposing continuity constraints in real and complex image correlation has been investigated. It is found that in regions where continuity can be assumed a second-order spline expansion of the underlying deformation field provides a globally smooth estimate of the deformation field. In general, only an estimate of the deformation at the subinterval centres needs to be provided from local correlation. If the assumption of continuity is violated multiple peaks in the correlation function are introduced. If the discontinuity exceeds one speckle diameter the correlation peaks will be separated, but with reduced correlation values. Otherwise, the different peaks will blend resulting in a deformed correlation function and a correlation value that approaches unity for small discontinuities. In this case, the Hessian is shown to provide a good estimate of the position of a discontinuity. Furthermore, a methodology to perform automatic remeshing is sketched. A subinterval edge is placed at the position of the detected discontinuity, the surrounding subintervals are reduced in size and the continuity constraint is relaxed. The methodology has proven successful on one-dimensional images but it can be transferred with reasonable effort to multi-dimensional images.

Analysis of Defect in Extreme UV Lithography Mask Using a Modal Method Based on Nodal B-Spline Expansion

This paper details to an electromagnetic modeling of an extreme ultraviolet (EUV) lithography mask. For that purpose, a modal method based on a spline nodal expansion (MMSNE) is presented. The results obtained using first, and second-order splines as basis functions are compared with those obtained using other modal methods, such as modal method by Fourier expansion (MMFE). The agreement between the results obtained using different methods is very good, and a convergence test is also performed. The spline nodal basis function implemented in this paper is the first step toward the realization of a multiresolution scheme that is expected to perform much more efficiently than conventional schemes.

A boundary element method for Laplace's equation without numerical integrations

A boundary element method (BEM), without any numerical integration, is presented here for the treatment of boundary value problems in Laplace's equation on a plane domain with a polygonal boundary. We use the double-layer potential to approximate the solution. The exact forms of the double-layer potentials for the first- and second-order spline density are to be derived here. These potentials can be differentiated directly. Then, the collocation method is applied to mixed boundary value problems. The collocation equations of the first-order scheme for Dirichlet's problems on a convex domain are shown to be well-conditioned; i.e., the condition number of the resulting matrix is bounded by a constant independent of the number of the elements. The second-order method can be applied to mixed boundary problems on interior and exterior regions. Two mixed boundary value problems with singular solutions are solved by the second-order scheme. Numerical examples show that the scheme is capable of dealing with singularities.

Shape coding using temporal correlation and joint VLC optimization

This paper investigates ways to explore the between frame correlation of shape information within the framework of an operationally rate-distortion (ORD) optimized coder. Contours are approximated both by connected second-order spline segments, each defined by three consecutive control points, and by segments of the motion-compensated reference contours. Consecutive control points are then encoded predictively using angle and run temporal contexts or by tracking the reference contour. We utilize a novel criterion for selecting global object motion vectors, which improves the efficiency. The problem is formulated as a Lagrangian minimization and solved using dynamic programming. Furthermore, we employ an iterative technique to remove dependency on a particular variable length code and jointly arrive at the ORD globally optimal solution and an optimized conditional parameter distribution.

Unicity of best 𝐿₂ approximation by second-order splines with variable knots

Unicity of best 𝐿₂ approximation by second-order splines with variable knots