Probably a Distribution

This chapter is all about Carl Gauss, his life, and his accomplishments, including his work in plotting the orbits for Ceres, which he did while still a teenager and which set his reputation. The chapter tells, too, how and when he invented and used his method of least squares and of his dispute with Legendre on who invented it first. One of his most significant accomplishments is his devising (and proof) of the normal probability density function, or, more familiarly, the standard normal curve. This is described and its import and application to modern times is discussed. Also, there is a brief discussion of biographical events and details of his life, such as his reclusive nature in his hometown of Göttingen, and his caring for his ailing mother and then his first and second wives. Some details of his impact today and lasting accomplishments are also provided.

PENENTUAN THRESHOLD CITRA MULUT DENGAN METODE NORMAL PROBABILITY DENSITY FUNCTION (NPDF) GUNA MENDETEKSI MULUT PEMELAJAR

Identifikasi wajah merupakan masalah sulit terutama ketika informasi dari fitur wajah tidak cukup atau terbatas. Misalnya dalam segmentasi mulut pemelajar, dimana objek yang diamati tergolong rumit, terutama ciri utama wajah yaitu, mata, mulut, hidung. Pada penelitian ini mengusulkan Normal Probability Density Function (Normal PDF ) dalam melakukan segmentasi dan pemisahan background dan foreground. Dari hasil eksperimen segmentasi mulut pemelajar metode Normal Probability Density Function (Normal PDF) dapat memberikan hasil segmentasi lebih baik. Proses pengukuran nilai rata-rata MSE menggunakan metode Normal Probability Density Function (NPDF) sebesar 275.3953475 piksel. Untuk Proses pengukuran nilai rata-rata PSNR menggunakan metode Normal Probability Density Function (NPDF) sebesar 24.39017959 piksel. Dari nilai rata-rata PSNR terbukti metode Normal Probability Density Function (NPDF) baik dan layak digunakan untuk melakukan segmentasi citra pada mulut pemelajar.

Density Function Optimization for the Homogenized Energy Model of Shape Memory Alloys

In this paper, we present two methods for optimizing the density functions in the homogenized energy model (HEM) of shape memory alloys (SMA). The density functions incorporate the polycrystalline behavior of SMA by accounting for material inhomogeneities and localized interaction effects. One method represents the underlying densities for the relative stress and interaction stress as log-normal and normal probability density functions, respectively. The optimal parameters in the underlying densities are found using a genetic algorithm. A second method represents the densities as a linear parameterization of log-normal and normal probability density functions. The optimization algorithm determines the optimal weights of the underlying densities. For both cases, the macroscopic model is integrated over the localized constitutive behavior using these densities. In addition, the estimation of model parameters using experimental data is described. Both optimized models accurately and efficiently quantify the SMA’s hysteretic dependence on stress and temperature, making the model suitable for use in real-time control algorithms.