Gravity Inversion for Heterogeneous Sedimentary Basin with b-Spline Polynomial Approximation using Differential Evolution Algorithm

A MATLAB-based inversion program, b-Spline Polynomial Approximation using Differential Evolution Algorithm (SPODEA), is introduced to recover the concealed basement geometry under heterogeneous sedimentary basins. Earlier inversion techniques used the discretized subsurface interface topography into a grid of juxtaposed elementary prisms to estimate the basement depth of a basin. Such discretization leads to the failure of depth profile continuity and requires a higher number of inversion parameters for achieving the desired accuracy. The novel approach of SPODEA overcomes such limitations of earlier inversion techniques. SPODEA is based on the segment-wise b-spline optimization technique to estimate the basement depth by using high-order polynomials.Moreover, it can achieve an optimal misfit with a minimal parametric information, which reduces the computational expense. The proposed inversion approach uses the differential evolution (DE) algorithm that provides real parametric optimization and uses b-splines for an accurate estimation of continuous depth profiles. The efficiency of the proposed algorithm is illustrated with two complex synthetic sedimentary basin models comprised of constant and depth varying density distributions. Furthermore, the uncertainty analysis of the proposed inversion technique is evaluated by incorporating white Gaussian noise into the synthetic models. Finally, the utility of SPODEA is illustrated by inverting gravity anomalies for two different real sedimentary basins. It produces geologically reasonable outcomes that are in close agreement with basement structures from previously reported results.

Fuzzy Cubic Spline Interpolation with Triangular Fuzzy Numbers

In applied mathematics, the salient and engrossing aspect is how to best approximate a function in a given space. In this paper a cubic spline polynomial approximation as best approximations of fuzzy function on a discrete set of points. In this work a novel approach is adopted to show this method using Triangular fuzzy numbers.

MODEL SPLINE KUBIK DENGAN TITIK-TITIK KNOTS DALAM REGRESI NONPARAMETRIK

Let a nonparametric regression model , where is respons variable, is regression curve that assumed an unrestricted form and contained in Sobolev space . For estimate curve is obtained by minimizing the Penalized Least Square (PLS). In this case given cubic spline polynomial approaching for optimal knots points, by using Generalized Cross Validation (GCV) method, to obtained optimal estimation model for regression curve. This application of cubic spline using bread turnover data from CV DEDE MAKASSAR. Based on analysis obtained four optimal knots on the months 3, 6, 8, and 11 by estimation equation as follows : Keywords : PLS, cubic spline, optimal knots, GCV.

Regresi Spline Polynomial Truncated Biprediktor untuk Identifikasi Perubahan Jumlah Trombosit Pasien Demam Berdarah Dengue

This paper is a longitudinal study using a nonparametric regression model to identify changes in platelet count from dengue fever. Changes in platelet counts were analyzed based on treatment time and hematocrit count factors. The estimator method proposed is spline polynomial truncated bipredictor. Based on the results of the simultaneous model estimation, we obtained GCV = 714.72 and R2 = 95.9%, it means the model is feasible to explain and identify changes in platelet count based on the time of treatment and the number of hematocrit from DBD patients. Based on the data, there are four patterns of platelet change based on time of treatment and three patterns of platelet change based on hematocrit that are different from each other.Abstrak:Paper ini merupakan studi longitudinal dengan menggunakan model regresi nonparametrik untuk mengidentifikasi perubahan jumlah trombosit demam berdarah. Perubahan jumlah trombosit dianalisis berdasarkan faktor waktu perawatan dan jumlah hematokrit. Metode estimator yang diusulkan adalah spline polynomial truncated bi prediktor. Berdasarkan hasil taksiran model simultan diperoleh GCV = 714,72 dan R2 = 95,9%, artinya model layak untuk menjelaskan dan mengidentifikasi perubahan jumlah trombosit berdasarkan waktu perawatan dan jumlah hematokrit pasien DBD. Berdasarkan data, terdapat empat pola perubahan trombosit berdasarkan waktu perawatan dan tiga pola perubahan trombosit berdasarkan hematokrit yang berbeda satu sama lain.

New method for solving a class of fractional partial differential equations with applications

In this work we suggest a numerical approach based on the B-spline polynomial to obtain the solution of linear fractional partial differential equations. We find the operational matrix for fractional integration and then we convert the main problem into a system of linear algebraic equations by using this matrix. Examples are provided to show the simplicity of our method.