Powerlaws Archives. By Bill Heil and Mikolaj Piskorski Twitter has attracted tremendous attention from the media and celebrities, but there is much uncertainty about Twitter's purpose.
Is Twitter a communications service for friends and groups, a means of expressing yourself freely, or simply a marketing tool? We examined the activity of a random sample of 300,000 Twitter users in May 2009 to find out how people are using the service. We then compared our findings to activity on other social networks and online content production venues. Our findings are very surprising. Of our sample (300,542 users, collected in May 2009), 80% are followed by or follow at least one user.
Although men and women follow a similar number of Twitter users, men have 15% more followers than women. Even more interesting is who follows whom. These results are stunning given what previous research has found in the context of online social networks. At the same time there is a small contingent of users who are very active. Metabolic Rate and Kleiber's Law. An explanation for this kind of relationship was proposed further back in 1883:Suppose the organism has a size of L, then the surface area A L2, while the volume V L3 assuming that it is in the shape of a sphere.If the density in the organism M / L3 is constant, then L M1/3, where M is the total mass of the organism.Since the heat dissipation from an organism is proportional to its surface area, the total metabolic rate R L2 M2/3, which is close but not quite the same as the 3/4 power-law.
Effort has been made to derive the 3/4 power-law for a broader category that includes plants, animals, and even one-celled organisms lacking a vascular system. The latest derivation is based mostly on geometry, particularly the hierarchical nature of circulatory networks. Table 01 The 1/4 Power-Law A 2008 research indicates that most organisms' metabolisms are clustered between 1 and 10 watts per kgm of mass. It seems that an optimum metabolic rate is located within this range. L. How Animals Avoid Each Other. +Enlarge image National Geographic/Punchstock A foraging spider monkey appears to follow a specific kind of “random walk” that optimizes its chances for finding food.
Now theoretical work in the 5 November Physical Review Letters explores how this type of motion may help these monkeys, as well as other animals, avoid unfriendly encounters with competitors or predators. The theory predicts how long it would take for different foraging animals to meet up, but the formalism could also help in understanding the dynamics of physical systems such as chemical reactions in turbulent environments. The standard example of a random walk is a drunk man stumbling away from the bar in random directions for each step. Much of the vicious walker research has dealt with Brownian motion, in which the length of each random step is roughly the same.
As expected, they found that encounters were extremely rare when walkers had three dimensions to explore. –Michael Schirber References N. Lévy flight. The term "Lévy flight" was coined by Benoît Mandelbrot,[1] who used this for one specific definition of the distribution of step sizes. He used the term Cauchy flight for the case where the distribution of step sizes is a Cauchy distribution,[2] and Rayleigh flight for when the distribution is a normal distribution[3] (which is not an example of a heavy-tailed probability distribution).
Later researchers have extended the use of the term "Lévy flight" to include cases where the random walk takes place on a discrete grid rather than on a continuous space.[4][5] A Lévy flight is a random walk in which the steps are defined in terms of the step-lengths, which have a certain probability distribution, with the directions of the steps being isotropic and random. The particular case for which Mandelbrot used the term "Lévy flight"[1] is defined by the survivor function (commonly known as the survival function) of the distribution of step-sizes, U, being[6] for some k satisfying 1 < k < 3.