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In mathematics and computer science, a balanced Boolean function is a Boolean function whose output yields as many 0s as 1s over its input set. This means that for a uniformly random input string of bits, the probability of getting a 1 is 1/2.
Brute force consists of checking all assignments of zeros and ones and counting those that have balanced rows and columns (n / 2 zeros and n / 2 ones). As there are 2 n 2 {\displaystyle 2^{n^{2}}} possible assignments and ( n n / 2 ) n {\displaystyle {\tbinom {n}{n/2}}^{n}} sensible assignments, this strategy is not practical except maybe up to ...
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...
In the mathematical field of real analysis, a simple function is a real (or complex)-valued function over a subset of the real line, similar to a step function. Simple functions are sufficiently "nice" that using them makes mathematical reasoning, theory, and proof easier. For example, simple functions attain only a finite number of values.
The softmax function, also known as softargmax [1]: 184 or normalized exponential function, [2]: 198 converts a vector of K real numbers into a probability distribution of K possible outcomes. It is a generalization of the logistic function to multiple dimensions, and is used in multinomial logistic regression .
In mathematics, the Milne-Thomson method is a method for finding a holomorphic function whose real or imaginary part is given. [1] It is named after Louis Melville Milne-Thomson . Introduction