From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature

Reed, William J.; Hughes, Barry D.

doi:10.1103/physreve.66.067103

Cited by 236 publications

(176 citation statements)

References 18 publications

(10 reference statements)

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“…Mathematical models have shown that a system with this description will produce a Pareto distribution (Reed & Hughes, 2002).…”

Section: Control Of Variation By Reward Probability 29 March 2004 Vermentioning

confidence: 98%

Control of Variation by Reward Probability.

Gharib¹,

Gade²,

Roberts³

2004

Journal of Experimental Psychology: Animal Behavior Processes

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Two bar-press experiments with rats tested the rule that reducing expectation of reward increases the variation from which reward selects. Experiment 1 used a discrete-trial random-interval schedule, with trials signalled by light or sound. One signal always ended with reward; the other ended with reward less often. The two signals were randomly mixed. Bar-press duration (how long the bar is held down) varied more during the signal with the lower probability of reward. Experiment 2 closely resembled Experiment 1 but used a random-ratio schedule rather than a random-interval schedule.Again, bar-press duration varied more during the signal with the lower probability of reward. The results support the rule-the first well-controlled comparisons to do so. Control of Variation by Reward Probability 29 March 2004 version 3 Control of Variation by Reward ProbabilityInstrumental learning requires both variation and selection --variation of action, selection by reward of what works (Staddon & Simmelhag, 1971;Hull, Langman, & Glenn, 2001) --but few experiments have studied variation (Chance, 1999;Domjan, 1998;Lieberman, 1990;Pearce, 1997;Staddon & Cerutti, 2003). Yet it is plausible that variation depends on recent events, just as response rate does. If an animal's actions vary too little, it will not find better ways of doing things; if they vary too much, rewarded actions will not be repeated. So at any time there is an optimal amount of variation, which changes as the costs and benefits of variation change. Animals that do instrumental learning would profit from a mechanism that regulates variation so that the actual amount is close to the optimal amount. If such a mechanism exists, we know little about it.Experiments about variation have been rare partly because variation has been hard to measure. Antonitis (1951), for example, took "6,600 photographs of nosethrusting responses" (p. 275) to study variation in nose position. Herrnstein (1961) used a special apparatus with ten switches to measure the location of key pecks.Although most studies of variation have measured spatial variation (e.g., Balsam, Deich, Ohyama, & Stokes, 1998;Eckerman & Lanson, 1969;Ferraro & Branch, 1968;Neuringer, 2002), temporal variation may be much easier to measure. A few studies (Lacter & Corey, 1982;Margulies, 1961;Millenson, Hurwitz, & Nixon, 1961) have measured the variation of bar -press duration (how long the bar is held down). Rats can be trained to make bar presses of specified durations (e.g., Notterman & Mintz, 1965; Control of Variation by Reward Probability 29 March 2004 version 4Platt, Kuch, & Bitgood, 1973), so the variation measured by bar-press duration includes the variation from which reward selects.Our use of bar-press duration to study variation began with a puzzle involving rats trained with the peak procedure (Gharib, Derby, & Roberts, 2001). On most trials, food was given for the first bar press more than 40 sec after the start of the trial, at which point the trial ended. On some trials, however, no food was gi...

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“…Mathematical models have shown that a system with this description will produce a Pareto distribution (Reed & Hughes, 2002).…”

Section: Control Of Variation By Reward Probability 29 March 2004 Vermentioning

confidence: 98%

Control of Variation by Reward Probability.

Gharib¹,

Gade²,

Roberts³

2004

Journal of Experimental Psychology: Animal Behavior Processes

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“…Italian economist Vilfredo Pareto (1897) was the first to suggest it followed a "natural law" where the higher end of the wealth distribution is described by power law, P (w) ∼ w −1−α . Repeated empirical studies Levy Solomon (1997); ;Reed Hughes (2002) ;Aoyama Souma (2003) show that the power law tail exhibits a remarkable spatial and temporal stability and while the value of the exponent, α, may vary slightly, it changes little from the value ∼ 1.5.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of money and income distributions

Repetowicz

Hutzler

Richmond

2005

Physica A: Statistical Mechanics and its Applications

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We study the model of interacting agents proposed by Chatterjee (2003) that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation.We show that when all agents have the same fixed savings propensity, subject to certain well defined approximations defined in the text, these equations yield the conjecture proposed by Chatterjee (2003) for the form of the stationary agent wealth distribution.If the savings propensity for the equations is chosen according to some random distribution we show further that the wealth distribution for large values of wealth displays a Pareto like power law tail, ie P (w) ∼ w 1+a . However the value of a for the model is exactly 1. Exact numerical simulations for the model illustrate how, as the savings distribution function narrows to zero, the wealth distribution changes from a Pareto form to to an exponential function. Intermediate regions of wealth may be approximately described by a power law with a > 1. However the value never reaches values of ∼ 1.6 − 1.7 that characterise empirical wealth data. This conclusion is not changed if three body agent exchange processes are allowed. We conclude that other mechanisms are required if the model is to agree with empirical wealth data.

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“…The same result holds also if the sampled process is not deterministic, but grows exponentially in expectation [561]. This Version 1.0.3, typeset on model has the advantage of producing a heavy-tailed distribution in the transient state, as opposed to previous models that only produce such distributions asymptotically.…”

Section: End Boxmentioning

confidence: 48%

“…One such model postulates that the probability that a new page links to an existing one is proportional to the number of links the page already has [49,9]. Another more abstract model considers the observed system state as resulting from sampling individual processes that each grow exponentially [352,561] (or similarly, from an exponentially growing number of sources that each grows exponentially [207]). …”

Section: Usesmentioning

confidence: 99%

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Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

191

131

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Reliable performance evaluations require the use of representative workloads. This is no easy task since modern computer systems and their workloads are complex, with many interrelated attributes and complicated structures. Experts often use sophisticated mathematics to analyze and describe workload models, making these models difficult for practitioners to grasp. This book aims to close this gap by emphasizing the intuition and the reasoning behind the definitions and derivations related to the workload models. It provides numerous examples from real production systems, with hundreds of graphs. Using this book, readers will be able to analyze collected workload data and clean it if necessary, derive statistical models that include skewed marginal distributions and correlations, and consider the need for generative models and feedback from the system. The descriptive statistics techniques covered are also useful for other domains.

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From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature

Cited by 236 publications

References 18 publications

Control of Variation by Reward Probability.

Control of Variation by Reward Probability.

Dynamics of money and income distributions

Workload Modeling for Computer Systems Performance Evaluation

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