What is the origin of the S curve?
The "S Curve" concept was probably invented by the famous Greek sculptor Praxiteles, son of Kifissodotos, who lived in the 4th century BC. The Indian tribhanga ("three bend") pose is similar, but generally more pronounced, often with the neck also curved to one side.
Who really discovered the bell curve?
- BBC Science Focus Magazine Who really discovered the Bell Curve? The Gaussian Curve, commonly referred to as the Normal distribution, was utilised by Karl Friedrich Gauss and Abraham De Moire to solve statistical problems.
What is technology S-curve in product design?
In the course of Product Design and Development, the Technology S-Curve determines the performance in regards to time and effort. It assists in determining the level of maturity of the industry/product. Let us discuss more details on the Technology S-Curves.
What is the ‘S-curve’?
Technological innovation typically manifests themselves into a market along the ‘S’ curve. In case of product, the Product Metric (In the case of the bulb, lumens of light output per unit watt; efficiency) can be plotted as a function of time when each product was introduced. The metric value will naturally fall as an ‘S- curve’ in time.
Who invented the S-curve innovation?
8. S-Curve & Innovation • S-Curve is a measure of the speed of adoption of an innovation. First used by in 1903 by Gabriel Tarde, who first plotted the S-shaped diffusion curve. This process has been proposed as the standard life cycle of innovations can be described using the ‗S-Curve‗.
What is the S-curve theory?
In regards to business performance, S-Curve theory states that a business sustains slow growth at first (1st Phase), followed by rapid growth (2nd Phase), and finally with declining growth that plateaus (3rd Phase).
What is an S-curve in art called?
In modern art – specifically painting – the S-curve was used as a compositional technique in the 1700s. Back then it was called “Hogarth's Curve” as the British painter William Hogarth was its champion. It was he who first called the S-curve the line of beauty and the “basis of all great art”.
Why is it called an S-curve?
The reason it's called an s-curve is because the shape of the graph typically forms a loose, shallow “S.” (The shape, however, depends on the type of project, so other formations are possible.) An s-curve in project management is typically used to track the progress of a project.
What is S-curve evolution?
The S-curve shows the innovation from its slow early beginnings as the technology or process is developed, to an acceleration phase (a steeper line) as it matures and, finally, to its stabilisation over time (the flattening curve), with corresponding increases in performance of the item or organisation using it.
What is an S-curve innovation?
S-Curve of Innovation (Figure C in Exhibit-1) represents product performance, competitive advantage, or generated value over time. During the evolutionary change, performance starts from a slow initial phase, goes through an accelerated and scaled interval before it stabilizes and matures.
What is an S-curve in Greek?
In Ancient Greek and Roman sculpture, the S-curve is a traditional art concept where the figure's body and posture is depicted like a sinuous or serpentine manner.
What are the 5 phases of an S-curve?
Here are the stages of an S-curve in business:Initial slow growth. ... Rapid growth. ... Late-stage slow growth. ... Stationary demand. ... Make plans before the stationary growth stage. ... Maintain a healthy corporate environment.
Why is S-curve important in photography?
'S-curve in photography is an image composition technique for photographers. According to this rule, the S-curve in a scene helps draw the viewer's attention to the image. It acts as a guideline connecting the viewer to the subject, thereby making the picture meaningful. In addition, it helps to make the image dynamic.
Who developed the S-curve and why?
The S-curve framework is not a new concept. The management thinker Charles Handy first applied it, also known as life cycle thinking or the “sigmoid curve,” to organizational and individual development in the mid-1990s. 1.
When did the S-curve come out?
2000S-Curve RecordsFounded2000FounderSteve GreenbergDistributor(s)Alternative Distribution Alliance (back catalog) Universal Music Group (2021–present)Country of originUnited States2 more rows
What is J curve and S-curve?
Two types of population growth patterns may occur depending on specific environmental conditions: An exponential growth pattern (J curve) occurs in an ideal, unlimited environment. A logistic growth pattern (S curve) occurs when environmental pressures slow the rate of growth.
When did the S curve start?
The origin of the S curve or logistic curve goes way back, namely into the studies of population growth by Pierre-François Verhulst in 1838 . Verhulst was influenced by Thomas Malthus’ “An Essay on the Principle of Population”, and showed that growth of a biological population is self-limiting by the finite amount of available resources. The logistic equation is also sometimes called the Verhulst-Pearl equation following its rediscovery in 1920. Alfred J. Lotka derived the equation again in 1925, calling it the law of population growth.
Who wrote the diffusion of innovations?
50 years ago today (2012), Everett Rogers published his book Diffusion of Innovations in which he described the lifecycle of innovations. His theory of innovation has become a standard model in the marketing world, and has been further developed from an explanatory model to a marketing tool, aimed at influencing speed of take up and penetration of innovations.
Who was the first to study diffusion theory?
He observed that the rate of “imitation” or adoption of a new idea usually followed an s-shaped curve over time. Rogers recognized Tarde as the first author on diffusion theory research.
What is the van Genuchten Gupta model?
The van Genuchten–Gupta model is based on an inverted S-curve and applied to the response of crop yield to soil salinity .
Why do TItration curves have sigmoid shapes?
Titration curves between strong acids and strong bases have a sigmoid shape due to the logarithmic nature of the pH scale .
What is the range of sigmoid curves?
Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals ...
Is a sigmoid convex or concave?
A sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0.
What is the S curve in technology?
Technological innovation time cycle and market behaviour are well characterized by the ‘S’ curve. Technological innovation typically manifests themselves into a market along the ‘S’ curve. In case of product, the Product Metric (In the case of the bulb, lumens of light output per unit watt; efficiency) can be plotted as a function of time when each product was introduced. The metric value will naturally fall as an ‘S- curve’ in time.
When does the S curve start?
Usually, when the innovation in the product reaches its maturity level, there might be a change in the technology which disrupts the industry or the market by its new technology. So thereby a new S-curve starts.
What happens when the new S curve starts?
When the new S-Curve starts, there will be a discontinuity in between the two S-Curves.
What is the purpose of a technology curve?
In the course of Product Design and Development, the Technology S-Curve determines the performance in regards to time and effort. It assists in determining the level of maturity of the industry/product. Let us discuss more details on the Technology S-Curves.
What is the S curve of innovation?
The Technology S-Curve of Innovation/product life cycle is a robust framework that can be used to analyze various products at their different stages and to explain their successes and failures. If you still have any further thoughts on this topic, please let us know in the comment section below.
When evaluating a product or an industry, it is crucial to understand where it is on the S-curve?
When evaluating a product or an industry, it is crucial to understand where it is on the S-curve due to the many implications that result out of that such as the possible risks and pitfalls that are associated for certain phases on it.
Who invented cassette tape?
At the start, at the fermenting stage, there was the Cassette tape which was invented by Phillips.
Who discovered the Bell curve?
Who really discovered the Bell Curve? The Gaussian Curve, commonly referred to as the Normal distribution, was utilised by Karl Friedrich Gauss and Abraham De Moire to solve statistical problems.
Who was the French math teacher who came up with the same curve?
But a French maths teacher named Abraham de Moivre arrived at the same curve decades earlier while tackling a problem that had baffled mathematicians for years: how to calculate the frequency that heads or tails appear over the course of many coin-tosses.
What is the Bell Curve?
By Robert Matthews. With its central peak and gracefully sloping sides, the Bell Curve is one of the best-known and important graphs in maths and science. Put simply, it shows the spread of values of anything affected by the cumulative effects of randomness.
What is the definition of the Gaussian curve?
Most mathematicians refer to the curve simply as the ‘Normal distribution’, while historians often use the term ‘Gaussian Curve’ as an example of Stigler’s Law of Eponymy, which states that no scientific discovery is named after its actual discoverer.
Who invented the curveball?
A clamshell on a Brooklyn beach inspired Candy Cummings to invent a pitch that still vexes batters more than 150 years later: the curveball.
Who said it would be a good joke on the boys if I could make a baseball curve the same way?
Cummings later wrote, “All of a sudden, it came to me that it would be a good joke on the boys if I could make a baseball curve the same way.”
Overview
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula:
Other standard sigmoid functions are given in the Examples section. In some f…
Definition
A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a non-negative derivative at each point and exactly one inflection point. A sigmoid "function" and a sigmoid "curve" refer to the same object.
Properties
In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the integral of any continuous, non-negative, bell-shaped function (with one local maximum and no local minimum, unless degenerate) will be sigmoidal. Thus the cumulative distribution functions for many common probability distributions are sigmoidal. One such example is the error function, which is related to the cumulative distribution function of a normal distribution; …
Examples
• Logistic function f ( x ) = 1 1 + e − x {\displaystyle f(x)={\frac {1}{1+e^{-x}}}}
• Hyperbolic tangent (shifted and scaled version of the logistic function, above) f ( x ) = tanh x = e x − e − x e x + e − x {\displaystyle f(x)=\tanh x={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}}}
Applications
Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a specific mathematical model is lacking, a sigmoid function is often used.
The van Genuchten–Gupta model is based on an inverted S-curve and applied t…
See also
• Heaviside step function
• Logistic regression
• Logit
• Softplus function
• Soboleva modified hyperbolic tangent
Further reading
• Mitchell, Tom M. (1997). Machine Learning. WCB McGraw–Hill. ISBN 978-0-07-042807-2.. (NB. In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural nets.)
External links
• "Fitting of logistic S-curves (sigmoids) to data using SegRegA". Archived from the original on 2022-07-14.