Youtor
Long Tail Distributions
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=vIp1kY0H0yw
Find the complete course at the Si Network Platform → https://bit.ly/NonlinearSystemsLearning • One result of the power laws that we discovered in the previous section are long tail distributions which is a type of graph we get when we plot a power law relation between two things. The long tail distribution, sometimes called the fat tail, is so called because it results in there being an extraordinarily large amount of small occurrences to an event and a very few very large occurrences with there being no real average or normal to the distribution. • Part of our definition for linear systems is that the relationship between input and output is related in a linear fashion, the ratio of input to output might be 2 times as much, 10 times as much or even a thousand times it is not important this is merely a quantitative difference, what is important is that this ratio between input and output is itself not increasing or decreasing. But as we have seen when we have feedback loops the previous state to the system feeds back to effect the current state thus enabling the current ration between input and output to be greater or less than its ratio previously and this is qualitatively different. • This phenomenon is captured within mathematical notation as an exponential. The exponential symbol describe how we take a variable and we times it by another not just once but we in fact iterate on this process, meaning we take that output and feed it back into compute the next output, thus the amount we are increasing by each time itself increases. So lets take a quick example of exponential grow to give you an intuition for it. • Say I wish to create a test tube of penicillin bacteria. Knowing that the bacteria will double every second, I start out in the morning with only two bacteria hoping to have my tube full by noon. As we know the bacteria will grow exponentially as the population at any time will feed into effect the population at the next second, like a snowball rolling down a hill. It will take a number of hours before our tube is just 3% full but within the next five seconds as it approaches noon it will increase to 100% percent of the tube... • Learn about the Systems Innovation Network on our social media: • → Twitter: http://bit.ly/2JuNmXX • → LinkedIn: http://bit.ly/2YCP2U6
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