Natural selection uses duplicated genes as raw material for functional innovation, co-opting their existing features to new functions. Understanding genetic innovation requires two questions to be ...

Graphing a piecewise defined function might seem daunting at first, but breaking down the process into manageable steps can make it significantly easier. A piecewise function, as the name suggests, is ...

A piecewise function is defined by multiple sub-functions, each applicable over a specific interval of the domain. These intervals are often called "pieces" of the function's domain. Each piece ...

Abstract: Neural networks (NNs) are commonly used to approximate functions based on data samples, as they are a universal function approximator for a large class of ...

Abstract: One of the most important properties of neural nets (NNs) for control purposes is the universal approximation property. Unfortunately,, this property is generally proven for continuous ...

Combined functions involve the operations of addition, subtraction, multiplication and division applied to two or more functions. A hybrid function is also an example of combined functions. Combined ...

Functions are fundamental in mathematics, describing relationships between inputs and outputs. For instance, linear functions are used to describe proportional relationships such as calculating cost ...

The tangent is defined as the single point where a straight line meets a curved surface. The tangent can be determined with a collection of mathematical formulas but is most commonly determined by ...