In this paper, two basis kernel functions are used, a polynomial function and a Gaussian function
, the latter of which is another form of radial basis function (RBF).
GOFT measurement is calculated as the normalized least mean square error between the best Gaussian function
that fits the histogram bins and the interpolation function constituted by bins center.
For this function, we take two-dimensional Gaussian function
. Each Gaussian function
for the attractive force is rotated along line segment connecting previous (i -1) and current i nodal points.
This operator is produced from the modification of the generalized Hermite sampling with Gaussian function
[mathematical expression not reproducible].
The fuzzy Gaussian function
of the population locus approximation is obtained by extracting the mean value at which the mean value of the fuzzy Gaussian population locus is the STR-DNA value of the most population density and deviation of the particular population.
The activation function of the hidden layer in this process was constructed by using a Gaussian function
These distributions are fitted with the double Gaussian function
as given in equation (6) of "Charged Particle, Photon Multiplicity, and Transverse Energy Production in High-Energy Heavy-Ion Collisions," which are represented by solid lines.
The GF is essentially a 2D convolution operator that uses the kernel that represents the shape of a Gaussian function
. The formula of a Gaussian function
in a 2D space is given as follows:
"We discovered that there is -- and, surprisingly, the variation in how branches are distributed in space can be described mathematically by something called a Gaussian function
, which is also known as a bell curve."
Electrical engineers present their research results on the modal analysis of microelectromechanical systems using ultrasonic base excitation, decentralized fault detection in wireless sensor network based on Gaussian function
error, the static behavior analytic and numerical analysis of micro-machined thermal accelerometers, a clamped-clamped beam resonator capacitive magnetometer based on a microelectromechanical system, extending the range for single hop wireless sensor networks with wake-up receivers, and a HW/SW implementation of FPGA of absolute robot localization using webcam data.
A function f(r) (r [member of] [R.sup.3]) can be approximated using Gaussian radial basis functions (RBFs) by [[??].sub.N](r) = [[summation].sup.N.sub.i=1] [[omega].sub.i][K.sub.[sigma]]([parallel]r - [r.sub.i][parallel]), where [K.sub.[sigma]](r) is the RBF kernel that is a Gaussian function
with the standard deviation [sigma] and the amplitude of 1, to which we refer as pseudoatom, N is the number of pseudoatoms, [r.sub.i] is the vector of the center coordinates of the ith pseudoatom, [parallel]r - [r.sub.i][parallel] is the Euclidean distance between the vectors r and [r.sub.i], and [[omega].sub.i] and > 0 is the weight (contribution) of the ith pseudoatom.
demonstrates random optical field with special autocorrelation which is different from the general autocorrelation with a Gaussian function
. The speckle with special autocorrelation has self-healing effect.