Radial Basis Functions (RBFs) are commonly used for interpolating scattered data, in numerical meshfree simulation methods, and in artificial neural networks

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### Which values of the exponent yield only real values of this function on the given domain

Given the following function: $$y = \frac{x^p}{x^p + (1 - x)^p},$$ where $x,p\in\mathbb{R}$, I want to know which values of $p$ yields $y\in\mathbb{R}$ for all $x$. Can anyone help me with this? ...
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### Approximating the inverse of a stochastic function

Assume that I have a stochastic function $f(x)=g(x)+\epsilon$, where $f:\mathbb{R}^D\rightarrow \mathbb{R}^D$ is composed of a deterministic function $g:\mathbb{R}^D\rightarrow \mathbb{R^D}$ and some ...
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### finding best fit surface passing through points using RBF or bspline methods

I have some points in 3D (x, y and z) and want to fit a surface through them. I prefer to use bsplines for finding the best surface among my points. My final goal is the equation of the surface. I ...
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### Interpolation with RBF

I have a function that is continuous and differentiable over $\mathbb{R}$ and its support is the whole real line. I want to approximate it through a linear combination of Gaussian functions. I know ...