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Topic: Power laws

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	Power law - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		where a (the constant of proportionality) and k (the exponent of the power law) are constants.
		Power laws are observed in many fields, including physics, biology, geography, sociology, economics, linguistics and war and terrorism.
		Power laws are among the most frequent scaling laws that describe the scale invariance found in many natural phenomena.
	en.wikipedia.org /wiki/Power_law (222 words)

	I/CI - isss98power.htm (Power Laws presentation)
		Power Laws analog some patterns and seem like predictive rules, but should be utilized with caution (e.g., phototropism, which in the surface looks like a direct correlation between light and subsequent plant growth, is in fact a result of metabolic actions reliant on durations of darkness and shade.)
		A power law can be applied to behavior of people in groups, or the behavior of stars in a galaxy, or the molecules in a container, but there is no current formulation which gets you from one domain to any of the others.
		Briefly, the new class Power Laws are exampled by the proportionality that says that "the distribution entropy of a set of components that are in recursive exchange between agents is inversely proportional to the entropy of the behavior-space of the agents" (Rose 1973,1992).
	www.ceptualinstitute.com /uiu_plus/isss98/isss98power.htm (2101 words)

	Power Laws: Hype or Revelation? [ MAS 965 ] (Site not responding. Last check: 2007-11-05)
		The term "power law" has come to describe the organizing principle that very few nodes will maintain a large percentage of the links in a network.
		The ubiquity of power laws has been interpreted as a revelation that touches almost all fields; as a result a large number of papers have been written on this topic in a short period of time.
		This class aims to review the literature central to the study of power laws and give attention to the question of whether this theory is here to stay.
	powerlaws.media.mit.edu (913 words)

	Shirky: Power Laws, Weblogs, and Inequality
		Power law distributions, the shape that has spawned a number of catch-phrases like the 80/20 Rule and the Winner-Take-All Society, are finally being understood clearly enough to be useful.
		The linguist George Zipf observed that word frequency falls in a power law pattern, with a small number of high frequency words (I, of, the), a moderate number of common words (book, cat cup), and a huge number of low frequency words (peripatetic, hypognathous).
		Given the ubiquity of power law distributions, asking whether there is inequality in the weblog world (or indeed almost any social system) is the wrong question, since the answer will always be yes.
	www.shirky.com /writings/powerlaw_weblog.html (2354 words)

	Tipping Point, Power Laws, Linked, and Weblogs
		In Power Laws, Weblogs, and Inequality, Clay runs blogging through the power law mill, and the result is akin to running a cat through a Cuisinart: you get easily measured stuff that bears no resemblence to the subject of the study.
		A familiar way to think about power laws is the 80/20 rule: 80% of the wealth is controlled by 20% of the population.
		The R-squared for the linear equation is 0.31, 0.55 for the quadratic, and 0.99 for the power law equation.
	www.alpern.org /weblog/stories/2003/02/20/tippingPointPowerLawsLinkedAndWeblogs.html (6623 words)

	netvironments \| Power Laws, Discourse, and Democracy (Site not responding. Last check: 2007-11-05)
		Power laws produce scale free networks, whose distinguishing characteristic is the hierarchy of hubs along the curve of the distribution.
		Popularizations of power law distributions and the 80/20 rule have fastened onto the idea that winner-takes-all networks are, not just a special case of networks governed by power laws, but the state toward which they inevitably tend.
		Power law distributions track the constant traffic — a flow of influence and information — up and down as well as in and out, across scales.
	www.netvironments.org /blog/essays/powerLawsDiscourse (2678 words)

	Guardian Unlimited \| Life \| The formula for 'success'
		Traffic jams, to cite an unrelated dynamic, often seem to obey a power law, with jams involving k cars occurring with a probability roughly proportional to 1/k^m for an appropriate ^m.
		Zipf's Law relates the frequency of a word to its rank order k and states that a word's frequency in a written text is proportional to 1/k^1; that is, inversely proportional to the first power of k.
		Along various social dimensions, the dynamics underlying power laws may lead naturally to the development of a few large, powerful economic, media, and political elites and the disparities that result.
	www.guardian.co.uk /life/lastword/story/0,,1265949,00.html (797 words)

	Weblogs and power laws (kottke.org)
		I've also noticed the power law in effect in the inter-page links which occur on a wiki, which is interesting because links are typically made based on the merits of the information, and not due to either a cult of personality or simply high visibility.
		You can generate power law distributions where in circumstances where the probability that, say, a randomly selected web page will link to your page is an increasing function of the number of pages that have already linked to your page.
		I've been reading all of the articles on weblogs and the power laws, but they all seem to be built on an unsupported assumption: that linking to someone is a reliable and meaningful indicator of the reading habits of the link-from weblog.
	www.kottke.org /03/02/weblogs-and-power-laws (3533 words)

	LeanLegal Tutorial - Power of Attorney
		A power of attorney is a document which authorizes someone to act on your behalf in a number of matters ranging from negotiating cheques or promissory notes; purchasing, selling or dealing with stocks and bonds; collecting rents, profits or commissions; managing, buying or selling real estate, conducting business operations or deciding issues about personal care.
		Legislation in some states also permits a power of attorney to survive a donor's mental incapacity if there is explicit wording to that effect and if it is witnessed by someone other than the donee/agent or his or her spouse.
		The power of attorney may, however, terminate upon a committee being appointed for the donor under the current legislation in your jurisdiction.
	www.leanlegal.us /tutorials/power_attorney.asp (1270 words)

	Ross Mayfield's Weblog: Power Laws and Private Equity (Site not responding. Last check: 2007-11-05)
		Venture rules of thumb acknowledge the power law indirectly: such as there is only room for three players in a market and you really only want to own #1 or #2.
		Power laws exist in each of these markets (even salary and employee performance) and we are just beginning to understand how to manage emergence.
		The power laws of complexity science reveal that regularity and predictability are neither as regular nor as predictable as business leaders have come to believe.
	ross.typepad.com /blog/2004/03/power_laws_and_.html (1619 words)

	Carnegie Endowment - Power and Weakness
		On the all-important question of power - the efficacy of power, the morality of power, the desirability of power - American and European perspectives are diverging.
		Europe is turning away from power, or to put it a little differently, it is moving beyond power into a self-contained world of laws and rules and transnational negotiation and cooperation.
		Indeed, it has produced a powerful European interest in inhabiting a world where strength doesn't matter, where international law and international institutions predominate, where unilateral action by powerful nations is forbidden, where all nations regardless of their strength have equal rights and are equally protected by commonly agreed-upon international rules of behavior.
	denbeste.nu /external/Kagan01.html (10744 words)

	Thoughts and Poems: Government and Power Laws (Site not responding. Last check: 2007-11-05)
		There was a hierarchy of political power, with those governments closest to the people having the most power, and those farthest away having the least.
		The founding fathers of the United States stumbled upon the concept of power laws centuries before they were formulated in contemporary chaos theory.
		Extinctions follow power laws – there are many single-species extinctions, a few extinctions that take out several interrelated species, fewer that take out many species, and the rarest of all: mass extinctions.
	zatavu.blogspot.com /2004/10/government-and-power-laws.html (1104 words)

	P.S.: » On Tag Clouds, Metric, Tag Sets and Power Laws
		The fact that tag clouds only approximate power laws, means that if we try to express a tag cloud as a power law, we will be making an error, and although we might expect the error eventually to go to zero, at the beginning it might be quite massive.
		Not only the error between the tag cloud and the approximated power law increased, but also the error between the the tag cloud and the nearest power law increased, as the fact of having a new term starting the ascension made the whole tag cloud wiggle around from its powerlawness.
		Since a document can be approximated both as a power law and as a position inside the hypercube, then two document can be expressed as an ordered list of tags (and the steepness, but now we don’t need it), and the first terms are the more relevant for the position in the hypercube.
	blog.pietrosperoni.it /2005/05/25/tag-clouds-metric (3902 words)

	Inequality. Many-to-Many: (Site not responding. Last check: 2007-11-05)
		The result is still a power law distribution (the economist Vilfredo Pareto called the distribution "a predictable imbalance" and found it in all market economies), its just got a shallower slope, and an average that's further from the #1 position and closer to the median.
		A simple solution to the power law "problem" would be for someone to create a tempered popularity index which inverts the list so that the top blogs appear at the bottom of the list.
		I agree the power law of distribution is immutable, but I'm saying its application to large networks is not mandated, and there are several ideas, including Seb's about downward linking social conventions(which, like Daniel, appeals to me) that may provide methods of dealing with the issue.
	www.corante.com /many/archives/2004/01/13/inequality.php (4836 words)

	LeanLegal Tutorial - Power of Attorney
		For example, under the Power of Attorney Act of Manitoba if the power of attorney contains wording which states that it is irrevocable, then the power of attorney is not terminated upon the death of the donor.
		Legislation in Manitoba also permits a power of attorney to survive a donor's mental incapacity if there is explicit wording to that effect and if it is witnessed by someone other than the donee/agent or his or her spouse.
		In some provinces and states, a donee who acts under a terminated power of attorney may be liable to the donor for damages, even if the donee did not know the power was no longer valid.
	www.leanlegal.com /tutorials/power_attorney.asp (1315 words)

	Power Law (Site not responding. Last check: 2007-11-05)
		The pricing of electricity sold to the country's power grids has been a core issue in the law.
		But should Congress vote to amend the VAT law and temporarily exempt power and fuel from the tax, Ermita said MalacaÃ±ang would have no choice but to comply.
		In physics, a power law relationship between two scalar quantities x and y is any such that the relationship can be written as
	www.wikiverse.org /power-law (220 words)

	Zipf, Power-law, Pareto - a ranking tutorial
		That is the exponent of the power law distribution a = 1+k (where k is the Pareto distribution shape parameter).
		Troll and P. beim Graben (1998), "Zipf's law is not a consequence of the central limit theorem", Phys.
		Note that the shape parameter of the Pareto distribution, k, equals a-1, where a is the power law slope.
	www.hpl.hp.com /research/idl/papers/ranking/ranking.html (1699 words)

	The 48 Laws of Power \| MetaFilter
		She got to her "power position" by employing an almost opposite approach, and I doubt Matt would ever bestow power on someone that didn't have broad support from the community.
		Power is concerned with what has already happened; strength with what has yet to happen.
		Power refers to the freedom persons have within limits, strength to the freedom persons have with limits.
	www.metafilter.com /mefi/39527 (2509 words)

	Amazon.com: Books: The 48 Laws of Power (Site not responding. Last check: 2007-11-05)
		Anyone striving for psychological health will be put off at the start, but the authors counter, saying "honesty is indeed a power strategy," and "genuinely innocent people may still be playing for power." Amoral or immoral, this compendium aims to guide those who embrace power as a ruthless game, and will entertain the rest.
		Each law, with such allusive titles as "Pose as a Friend, Work as a Spy," "Get Others to Do the Work for You, But Always Take the Credit," "Conceal Your Intentions," is demonstrated in four ways?using it correctly, failing to use it, key aspects of the law and when not to use it.
		The author doesn't even try to formulate rules for when certain of the power "laws" are called for, and when their opposites would work (the "reversal" sections notwithstanding), he just rattles off all 48 one after the other.
	www.amazon.com /exec/obidos/tg/detail/-/0670881465?v=glance (2097 words)

	power_laws (Site not responding. Last check: 2007-11-05)
		Power laws are used by chronic bears to show that a stock market earthquake is bound to occur, and that distributions of prices are fat tailed, and that buying volatility works.
		My favorite discussion of how to deal with such laws simply: [ f(x) = x to -a power ] (where x is something like the number of people or stocks with income greater than x) is in Harold Thayer Davis' The Analysis of Economic Time Series.
		The answer is never, because power laws are one of those useless descriptive things that explains everything and makes one look sapient, and encourages people with money or respect to part with it, while aggrandizing and legitimizing your hatred of individual differences.
	www.dailyspeculations.com /vic/power_laws.html (239 words)

	The 48 Laws of Power
		Learn and apply the laws of courtiership and there will be no limit to how far you can rise in the court.
		There is great power in tapping into the fantasies of the masses.
		If you are new to a position of power, or an outsider trying to build a power base, make a show of respecting the old way of doing things.
	www.tech.purdue.edu /Cgt/Courses/cgt411/covey/48_laws_of_power.htm (3039 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		They're found in all kinds of places: - earthquake size - size of cities - community size on LiveJournal - fluctuation magnitude of a share price Power laws are characterised by a property: - the distribution looks the same, regardless of the scale you consider This is called scale invariance.
		That adjustment factor (four times as rare; four times the number of cities) isn't the important bit -- that can be any number as long as it stays the same regardless of the scale.
		So my hypothesis is that numbers picked randomly from a scarce resource will organise themselves into a power law distribution.
	www.interconnected.org /notes/2002/12/Origin_of_power_laws.txt (386 words)

	Notio: The power of power laws
		Clay Shirky has an interesting article on power laws.
		Most people know about power laws because of the "80/20" rule, or Pareto's law.
		It turns out that power laws accurately describe any social system "where many people are free to choose between many options" - his example is the popularity of webloggers, but the theory can be applied to many other important aspects of social life.
	www.notio.com /2003/02/the_power_of_power_laws.html (167 words)

	The 48 Laws of Power
		Mastery of one's emotions and the arts of deception and indirection are, he goes on to assert, essential.
		As attention--grabbing in its design as it is in its content, this bold volume outlines the laws of power in their unvarnished essence, synthesizing the philosophies of Machiavelli, Sun-tzu, Carl von Clausewitz, and other great thinkers.
		Some laws teach the need for prudence ("Law 1: Never Outshine the Master"), the virtue of stealth ("Law 3: Conceal Your Intentions"), and many demand the total absence of mercy ("Law 15: Crush Your Enemy Totally"), but like it or not, all have applications in real life.
	www.coolteenbooks.com /h/History/The_48_Laws_of_Power_0140280197.htm (260 words)

	IDblog: Tilting at power laws
		Over on the AIfIA list, Christina asked if anyone has tried to change the curve inherent in a power law and/or whether it was worth doing.
		I suspect that most efforts to "change" the power law (e.g., this one) are really only effective at moving individual objects up or down the curve...they don't really change the shape of the curve itself.
		IDblog is Beth Mazur tilting at power law windmills.
	www.idblog.org /archives/000121.html (250 words)

	O'Reilly Open Source Convention 2004
		"Power laws" are increasingly used to describe an organizing feature of networks as diverse as infectious disease transmission, the World Wide Web, airport hubs-and-spokes, actors in movies, and corporate boards of directors.
		These "scale-free" networks behave according to certain principles: (1) a small number of nodes control a large percentage of links, and (2) evolution of the network is dependent upon complex "preferential growth" models.
		This talk introduces power laws in open source development, similarities to other known power law networks, and the implications of power laws for predicting certain events in the evolution of open source development networks.
	conferences.oreillynet.com /cs/os2004/view/e_sess/5121 (260 words)

	Fluctuations and Power Laws in Pulmonary Physiology -- Suki 166 (2): 133 -- American Journal of Respiratory and ...
		power laws are ubiquitous in nature (2, 3).
		For Model A, the distribution is a power law (31), as evidenced
		is a power law with exponent 2 (40), the probability that 100
	ajrccm.atsjournals.org /cgi/content/full/166/2/133 (3903 words)

	Power Laws and Blogs
		The easiest way to see a power law is to plot the data in log/log space.
		Here we can clearly see a saturation effect - the power law breaks down after a while, as there are feedback mechanisms in place for movies (they won't show a second week if they gross poorly in the first).
		The green line sloping from top right to bottom left is Clay's power law, the red line from top left to bottom right is the number of blogs with that many incoming links.
	homepage.mac.com /kevinmarks/powerlaws.html (633 words)

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