Logistic functionS-shaped curve A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f(x)=L1+e−k(x−x0){\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}}where L{\displaystyle L} is the carrying capacity, the supremum of the values of the function;k{\displaystyle k} is the logistic growth rate, the steepness of the curve; andx0{\displaystyle x_{0}} is the x{\displaystyle x} value of the function's midpoint.The logistic function has domain the real numbers, the limit as x{\displaystyle x} tends to −∞{\displaystyle -\infty } is 0, and the limit as x{\displaystyle x} tends to +∞{\displaystyle +\infty } is L{\displaystyle L}.
Heaviside step functionThe Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.
Monotonic functionIn mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysisIn calculus, a function f{\displaystyle f} defined on a subset of the real numbers with real values is called monotonic if it is either entirely non-decreasing, or entirely non-increasing.
Artificial neuronAn artificial neuron is a mathematical function conceived as a model of a biological neuron in a neural network. The artificial neuron is the elementary unit of an artificial neural network. The design of the artificial neuron was inspired by biological neural circuitry. Its inputs are analogous to excitatory postsynaptic potentials and inhibitory postsynaptic potentials at neural dendrites, or activation.Graph of a functionIn mathematics, the graph of a functionf{\displaystyle f} is the set of ordered pairs(x,y){\displaystyle (x,y)}, where f(x)=y.{\displaystyle f(x)=y.} In the common case where x{\displaystyle x} and f(x){\displaystyle f(x)} are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve. The graphical representation of the graph of a function is also known as a plot.
Hyperbolic functionsHyperbolic analogues of trigonometric functionsIn mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.
Activation functionIn artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and their weights. Nontrivial problems can be solved using only a few nodes if the activation function is nonlinear.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
SpillwayA spillway is a structure used to provide the controlled release of water from a dam or levee, typically downstream into the dammed river. In the United Kingdom, it may be known as an overflow channel. A spillway ensures that water does not damage parts of the structure not designed to convey water. Spillways can include floodgates and fuse plugs to regulate water flow and reservoir level.Gompertz functionThe Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the curve than the left-side or lower valued asymptote.Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.DamA dam is a structure that impounds water or restricts its flow.
Neural network (machine learning)In machine learning, a neural network (NN) or artificial neural network (ANN) is a computational model inspired by the structure and functions of biological neural networks. A neural network consists of connected units or nodes called artificial neurons, which loosely model the neurons in the brain. These are connected by edges, which model the synapses in the brain.*As an Amazon Associate I earn from qualifying purchases.