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Sigmoid function (Sigmoid function) is a mathematical function living alone that the form of the English letter "S" (sigmoid curve). Often, sigmoid function refers to the special case of the logistic function living alone is shown in the first figure is defined by the formula
Another example is the Gompertz curve. Focaccia sigmoid living alone models used in systems that have a value which expanded rapidly in the field of initial t but then reach saturation when t increases. living alone Another example is the ogee curve as used in the spillway of several dams.
A wide range of the sigmoid function is used for describing functions of the operating system of artificial neurons, including logistic and hyperbolic tangent functions. Sigmoid curves are also common cumulative distribution statistics as functions as integrals of the logistic distribution, normal distribution and density functions of the distribution of t.
Sigmoid function similar functions that occurs in many cases where there is positive feedback loops initially causes a rapid growth of some value, and then we went into action feedback loops weaken slowing growth. These examples include: Physics and Chemistry
Response speed of the many chemical reactions similar function sigmoid process Aotoktliti - initially have many reactions between different molecules, and the reaction itself increases the probability of comments from other molecules in the sample due to the emission of byproducts, electronic keys undermine or heat helps post, below a concentration Hmoloklot drops and speed Examples decreasing population biology of bacterial growth in a petri dish - initially have rapid growth of the bacteria, and then there is an accumulation of waste materials and food restrictions are slowing the growth of bacteria. The growth of animals or plants of a species invades a new ecosystem - the species is expanding at the expense of other species to the limitations of food sources or predators begin to slow down population growth. Maximum running speed as a function of a person's age - first learn to crawl, walk and then run. The greater living alone the age of lengthening limbs and muscles living alone are growing and so can run faster. Then start the old processes affecting the heart, lungs and muscle living alone that cause slow decrease in maximum speed Rizzi. The growth of the human population before the Industrial Revolution in the sigmoid functions that a similar failure - initially the population is growing rapidly with the arrival to the island, and then resource constraints maintained a stable population. Examples economics of new product sales - initially just eager buyers buy the product and its sales are slow. Then if the product is good word of mouth marketing reach masses of people, or that the company has enough money to advertise the new product at this time accelerating sales. At this point you may also demand induced the increased demand with supply Lmmotzr. Then there is a slowdown in sales as almost all of the demand is covered. Average travel speed as a function of car town car number - initially slow cars have accelerated the speed, the more cars there are more problems with traffic jams and parking living alone slowed speed. Economies of scale economies of scale in many cases very helpful in a certain area, and then their benefits are weakened by the disadvantages of scale. Social welfare and economic growth. According to a number of philosophers (eg The Spirit living alone Level) and social welfare studies weakening in countries with higher economic output. That rich countries continued economic growth does not affect living alone social welfare, life expectancy and a great range of health living alone and social parameters.
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