Sign function

The sign function is a second activation function with an abrupt threshold T, this time set at zero input (Figure 2.9). The output from a node that uses this function is +1 if the input is zero or greater otherwise it is -1. 

Sign and Heaviside Step Functions We may define the sign function... 

The permanent, denoted by per(M), also referred to as positive determinant, is defined by omitting the sign function s(n) [Schultz et al, 1992 Yang et al., 1994 Cash, 1995a Cash, 1998] as ... 

The entries of the main diagonal are excluded from the calculation of the pfaffian and hafnian [Caianiello, 1953,1956]. Hafniansandpfaffians differ in the sign function s(jt) that is included in the definition of pfaffian only. 

Note that d t = -dts is not a necessary condition as it implies equal parental shares constituting the interface. It suffices to force dgn(dst) = -dgn(dts) where sign ) denotes the sign function. However, this generalization requires some more notation and, therefore, is not discussed here. 

Modified Sign Similar to the sign function, except that if /, = 0, then = 0. That is,... 

Step Function Similar to the sign function except the smallest value is 0, instead of -1. Thus, it is a binary logic unit. 

It has been noticed [37] that A is positive for any attractive power-law potential e(a)r , where e is the sign function. In particular, if the popular Coulomb-plus-linear potential is split into its best harmonic approximation (for N = 2) and a correction to it, say... 

However, this extrapolation of the line into the second quadrant immediately brings an inherent and up to now hidden problem in the theoretical derivation of Eq. (1), and thus of Eq. (12), sharply into focus. In the second quadrant, K is positive, and is negative, so that it follows that the quantum number n must necessarily be a complex number, in, where the — sign functions in the fourth quadrant so that is positive, and the -I- sign in the second quadrant where is negative ... 

A function file is a user-defined function using MATLAB. We use function files for repetitive tasks. The first line of a function file must contain the word function, followed by the output argument, the equal sign (=), function name, and the input argument enclosed in parentheses. The function name and file name must be the same, but the file name must have the extension. m. For example, the function file consisting of the following two lines... 

Manual call points according to safety plot plan, accessible, signed, functioning... 

As mentioned later, some methods of X-ray phase imaging allow us to measure 0d>(x, z)/3x. In such a case, one may get d)(x, z) through integration. However, it is possible to recon-stmct phase tomograms directly from the differential phase shift by using the sign function sgn(co) instead of the filter funaion [Pg.551]

---