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{{Redirect|Yule process|the type of birth process|Simple birth process}}

{{Redirect|Yule process|the type of birth process|Simple birth process}}

A classic example of a preferential attachment process is the growth in the number of species per genus in some higher taxon of biotic organisms.  New genera ("urns") are added to a taxon whenever a newly appearing species is considered sufficiently different from its predecessors that it does not belong in any of the current genera.  New species ("balls") are added as old ones speciate (i.e., split in two) and, assuming that new species belong to the same genus as their parent (except for those that start new genera), the probability that a new species is added to a genus will be proportional to the number of species the genus already has.  This process, first studied by Yule, is a linear preferential attachment process, since the rate at which genera accrue new species is linear in the number they already have.

A classic example of a preferential attachment process is the growth in the number of species per genus in some higher taxon of biotic organisms.  New genera ("urns") are added to a taxon whenever a newly appearing species is considered sufficiently different from its predecessors that it does not belong in any of the current genera.  New species ("balls") are added as old ones speciate (i.e., split in two) and, assuming that new species belong to the same genus as their parent (except for those that start new genera), the probability that a new species is added to a genus will be proportional to the number of species the genus already has.  This process, first studied by Yule, is a linear preferential attachment process, since the rate at which genera accrue new species is linear in the number they already have.

优先链接过程的一个典型例子是生物有机体的某些高级分类单元中每个属的物种数量的增长。每当一个新出现的物种被认为与其祖先完全不同，不属于任何一个现有属时，新属(“urns”)就被添加到分类单元中。新物种(“球”)加入的时候旧物种发生演变(即一分为二)，如果认为新物种与其亲本属于同一属(除外它们本身是新属)，那么新物种加入该属的概率将与该属已有的物种数量成正比。这个首先被Yule研究的过程，就是一个线性优先链接的过程，因为新物种的繁殖率与其已经拥有的数量成线性关系。

优先链接过程的一个典型例子是生物有机体的某些高级分类单元中每个属的物种数量的增长。<ref name=YulePhilTrans>{{cite journal | last=Yule | first=G. U. | title=A Mathematical Theory of Evolution, based on the Conclusions of Dr. J. C. Willis, F.R.S | journal=[[Philosophical Transactions of the Royal Society B]] | volume=213 | pages=21–87 | year=1925 | doi=10.1098/rstb.1925.0002 | issue=402–410| doi-access=free }}</ref>每当一个新出现的物种被认为与其祖先完全不同，不属于任何一个现有属时，新属(“urns”)就被添加到分类单元中。新物种(“球”)加入的时候旧物种发生演变(即一分为二)，如果认为新物种与其亲本属于同一属(除外它们本身是新属)，那么新物种加入该属的概率将与该属已有的物种数量成正比。这个首先被Yule研究的过程，就是一个线性优先链接的过程，因为新物种的繁殖率与其已经拥有的数量成线性关系。

Linear preferential attachment processes in which the number of urns increases are known to produce a distribution of balls over the urns following the so-called Yule distribution.  In the most general form of the process, balls are added to the system at an overall rate of m new balls for each new urn.  Each newly created urn starts out with k₀ balls and further balls are added to urns at a rate proportional to the number k that they already have plus a constant a&nbsp;>&nbsp;−k₀.  With these definitions, the fraction P(k) of urns having k balls in the limit of long time is given by

Linear preferential attachment processes in which the number of urns increases are known to produce a distribution of balls over the urns following the so-called Yule distribution.  In the most general form of the process, balls are added to the system at an overall rate of m new balls for each new urn.  Each newly created urn starts out with k₀ balls and further balls are added to urns at a rate proportional to the number k that they already have plus a constant a&nbsp;>&nbsp;−k₀.  With these definitions, the fraction P(k) of urns having k balls in the limit of long time is given by

翁的数量增加的线性优先链接过程，会在翁中按照所谓的Yule分布产生球的分布。在最一般形式的过程中，球添加到系统中的整体速率是每个瓮中添加m个新球。每个新创建的瓮都以 k₀ 个球开始，然后新球被不断地添加到瓮中，其速度与瓮的数量k加常数 ''a''&nbsp;>&nbsp;>−''k''₀成正比。利用这些定义，可以给出长时极限下具有k个球的瓮的分数P(k):

翁的数量增加的线性优先链接过程，会在翁中按照所谓的Yule分布产生球的分布。在最一般形式的过程中，球添加到系统中的整体速率是每个瓮中添加m个新球。每个新创建的瓮都以 k₀ 个球开始，然后新球被不断地添加到瓮中，其速度与瓮的数量k加常数 ''a''&nbsp;>&nbsp;>''k''₀成正比。利用这些定义，可以给出长时极限下具有k个球的瓮的分数P(k)<ref>{{cite journal | last=Newman | first=M. E. J. | title=Power laws, Pareto distributions and Zipf's law | journal=Contemporary Physics | volume=46 | pages=323–351 | year=2005 | arxiv=cond-mat/0412004 | doi=10.1080/00107510500052444 | issue=5 | bibcode=2005ConPh..46..323N}}</ref>:

In other words, the preferential attachment process generates a "long-tailed" distribution following a Pareto distribution or power law in its tail.  This is the primary reason for the historical interest in preferential attachment: the species distribution and many other phenomena are observed empirically to follow power laws and the preferential attachment process is a leading candidate mechanism to explain this behavior.  Preferential attachment is considered a possible candidate for, among other things, the distribution of the sizes of cities, the wealth of extremely wealthy individuals, and the number of links to pages on the World Wide Web.

In other words, the preferential attachment process generates a "long-tailed" distribution following a Pareto distribution or power law in its tail.  This is the primary reason for the historical interest in preferential attachment: the species distribution and many other phenomena are observed empirically to follow power laws and the preferential attachment process is a leading candidate mechanism to explain this behavior.  Preferential attachment is considered a possible candidate for, among other things, the distribution of the sizes of cities, the wealth of extremely wealthy individuals, and the number of links to pages on the World Wide Web.

换句话说，优先链接过程在其尾部产生一个遵循'''<font color="#ff8000">帕累托分布 Pareto Distribution</font>'''或'''<font color="#ff8000">幂定律 Power Law</font>'''的'''<font color="#ff8000">“长尾”分布 Long-Tailed Distribution</font>'''。这是历史上人们对优先链接感兴趣的主要原因: 经过实际的观察，物种分布和许多其他现象都遵循幂律分布，而优先链接过程是解释这种行为的主要候选机制。它还可能解释如城市规模的分布，大富豪的财富，以及万维网网页的链接数量等问题。

换句话说，优先链接过程在其尾部产生一个遵循'''<font color="#ff8000">帕累托分布 Pareto Distribution</font>'''或'''<font color="#ff8000">幂定律 Power Law</font>'''的'''<font color="#ff8000">“长尾”分布 Long-Tailed Distribution</font>'''。这是历史上人们对优先链接感兴趣的主要原因: 经过实际的观察，物种分布和许多其他现象都遵循幂律分布，而优先链接过程是解释这种行为的主要候选机制。它还可能解释如城市规模的分布<ref name=SimonBiomet>{{cite journal | last=Simon | first=H. A. | title=On a class of skew distribution functions | journal=Biometrika | volume=42 | pages=425–440  | year=1955 | doi=10.1093/biomet/42.3-4.425  | issue=3–4 }}</ref>，大富豪的财富<ref name=SimonBiomet /> the number of citations received by learned publications,<ref name=PriceJASIS>{{cite journal | last=Price | first=D. J. de S.  | title=A general theory of bibliometric and other cumulative advantage processes | journal=J. Amer. Soc. Inform. Sci. | volume=27 | pages=292–306 | year=1976 | url=http://garfield.library.upenn.edu/price/pricetheory1976.pdf | doi=10.1002/asi.4630270505 | issue=5}}</ref>，以及万维网网页的链接数量等问题。<ref name=BAScience>{{cite journal | last=Barabási | first=A.-L. |author2=R. Albert | title=Emergence of scaling in random networks | journal=Science | volume=286 | pages=509–512 | year=1999 | arxiv=cond-mat/9910332 | doi=10.1126/science.286.5439.509 | issue=5439 | pmid=10521342| bibcode=1999Sci...286..509B }}</ref>

The general model described here includes many other specific models as special cases.  In the species/genus example above, for instance, each genus starts out with a single species (k₀&nbsp;=&nbsp;1) and gains new species in direct proportion to the number it already has (a&nbsp;=&nbsp;0), and hence P(k)&nbsp;=&nbsp;B(k,&nbsp;γ)/B(k₀,&nbsp;γ&nbsp;−&nbsp;1) with γ=2&nbsp;+&nbsp;1/m.  Similarly the Price model for scientific citations corresponds to the case k₀&nbsp;=&nbsp;0, a&nbsp; =&nbsp;1 and the widely studied Barabási-Albert model corresponds to k₀&nbsp;=&nbsp;m, a&nbsp;=&nbsp;0.

The general model described here includes many other specific models as special cases.  In the species/genus example above, for instance, each genus starts out with a single species (k₀&nbsp;=&nbsp;1) and gains new species in direct proportion to the number it already has (a&nbsp;=&nbsp;0), and hence P(k)&nbsp;=&nbsp;B(k,&nbsp;γ)/B(k₀,&nbsp;γ&nbsp;−&nbsp;1) with γ=2&nbsp;+&nbsp;1/m.  Similarly the Price model for scientific citations corresponds to the case k₀&nbsp;=&nbsp;0, a&nbsp; =&nbsp;1 and the widely studied Barabási-Albert model corresponds to k₀&nbsp;=&nbsp;m, a&nbsp;=&nbsp;0.

这里描述的一般模型包括许多作为特例的其他特定模型。例如，在上面的种属例子中，每个属以一个单一的种(k₀&nbsp;=&nbsp;1)开始，并且获得的新种正比于它已有的种的数量(a&nbsp;=&nbsp;0) ，因此P(k)&nbsp;=&nbsp;B(k,&nbsp;γ)/B(k₀,&nbsp;γ&nbsp;−&nbsp;1)，γ=2&nbsp;+&nbsp;1/m. 。类似地，科学引文的'''<font color="#ff8000">价格模型 Price Model</font>'''对应于k₀&nbsp;=&nbsp;0，a&nbsp; =&nbsp;1 ，而广泛研究的'''<font color="#ff8000">Barabási-Albert 模型</font>'''对应于 k₀&nbsp;=&nbsp;m, a&nbsp;=&nbsp;0.。

这里描述的一般模型包括许多作为特例的其他特定模型。例如，在上面的种属例子中，每个属以一个单一的种(k₀&nbsp;=&nbsp;1)开始，并且获得的新种正比于它已有的种的数量(a&nbsp;=&nbsp;0) ，因此P(k)&nbsp;=&nbsp;B(k,&nbsp;γ)/B(k₀,&nbsp;γ&nbsp;−&nbsp;1)，γ=2&nbsp;+&nbsp;1/m. 。类似地，科学引文的'''<font color="#ff8000">价格模型 Price Model</font>'''<ref name=PriceJASIS /> 对应于k₀&nbsp;=&nbsp;0，a&nbsp; =&nbsp;1 ，而广泛研究的'''<font color="#ff8000">Barabási-Albert 模型</font>'''<ref name=BAScience />对应于 k₀&nbsp;=&nbsp;m, a&nbsp;=&nbsp;0.。

Preferential attachment is sometimes referred to as the Matthew effect, but the two are not precisely equivalent.  The Matthew effect, first discussed by Robert K. Merton, is named for a passage in the biblical Gospel of Matthew: "For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him." (Matthew 25:29, New International Version.)  The preferential attachment process does not incorporate the taking away part. This point may be moot, however, since the scientific insight behind the Matthew effect is in any case entirely different.  Qualitatively it is intended to describe not a mechanical multiplicative effect like preferential attachment but a specific human behavior in which people are more likely to give credit to the famous than to the little known.  The classic example of the Matthew effect is a scientific discovery made simultaneously by two different people, one well known and the other little known.  It is claimed that under these circumstances people tend more often to credit the discovery to the well-known scientist.  Thus the real-world phenomenon the Matthew effect is intended to describe is quite distinct from (though certainly related to) preferential attachment.

Preferential attachment is sometimes referred to as the Matthew effect, but the two are not precisely equivalent.  The Matthew effect, first discussed by Robert K. Merton, is named for a passage in the biblical Gospel of Matthew: "For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him." (Matthew 25:29, New International Version.)  The preferential attachment process does not incorporate the taking away part. This point may be moot, however, since the scientific insight behind the Matthew effect is in any case entirely different.  Qualitatively it is intended to describe not a mechanical multiplicative effect like preferential attachment but a specific human behavior in which people are more likely to give credit to the famous than to the little known.  The classic example of the Matthew effect is a scientific discovery made simultaneously by two different people, one well known and the other little known.  It is claimed that under these circumstances people tend more often to credit the discovery to the well-known scientist.  Thus the real-world phenomenon the Matthew effect is intended to describe is quite distinct from (though certainly related to) preferential attachment.

优先链接有时被称为马太效应，但两者并不完全等同。马太效应，最早由罗伯特·金·莫顿讨论，是根据《圣经》中的一段马太福音命名的: 凡有的，还要加给他，叫他有余；凡没有的，连他所有的也要夺去。(马太福音25:29，新国际版)。优先链接过程并不包括夺走的部分。但是这一说法可能没有意义，因为马太效应背后的科学见解无论如何都是不一样的。定性地说，它并不是像如优先链接一样在描述一种机械的乘法效应，而是在描述一种特定的人类行为。在这种行为中，人们更有可能给归功于名人而不是归功于小透明。马太效应的经典例子是：两个不同的人同时做出了某项科学发现，其中一个人十分有名，另一个人则鲜为人知；据称，在这种情况下，人们往往更倾向于将这一发现归功于著名的科学家。因此，马太效应所要描述的现实景象与优先链接是截然不同的(虽然肯定与优先链接有关)。

优先链接有时被称为马太效应，但两者并不完全等同。马太效应，最早由罗伯特·金·莫顿讨论<ref>{{cite journal | last=Merton | first=Robert K. | authorlink=Robert K. Merton | title=The Matthew effect in science | journal=Science | volume=159 | pages=56–63 | year=1968 | doi=10.1126/science.159.3810.56 | pmid=17737466 | issue=3810| bibcode=1968Sci...159...56M }}</ref>，是根据《圣经》中的一段马太福音命名的: 凡有的，还要加给他，叫他有余；凡没有的，连他所有的也要夺去。(马太福音25:29，新国际版)。优先链接过程并不包括夺走的部分。但是这一说法可能没有意义，因为马太效应背后的科学见解无论如何都是不一样的。定性地说，它并不是像如优先链接一样在描述一种机械的乘法效应，而是在描述一种特定的人类行为。在这种行为中，人们更有可能给归功于名人而不是归功于小透明。马太效应的经典例子是：两个不同的人同时做出了某项科学发现，其中一个人十分有名，另一个人则鲜为人知；据称，在这种情况下，人们往往更倾向于将这一发现归功于著名的科学家。因此，马太效应所要描述的现实景象与优先链接是截然不同的(虽然肯定与优先链接有关)。

The first rigorous consideration of preferential attachment seems to be that of Udny Yule in 1925, who used it to explain the power-law distribution of the number of species per genus of flowering plants.  The process is sometimes called a "Yule process" in his honor.  Yule was able to show that the process gave rise to a distribution with a power-law tail, but the details of his proof are, by today's standards, contorted and difficult, since the modern tools of stochastic process theory did not yet exist and he was forced to use more cumbersome methods of proof.

The first rigorous consideration of preferential attachment seems to be that of Udny Yule in 1925, who used it to explain the power-law distribution of the number of species per genus of flowering plants.  The process is sometimes called a "Yule process" in his honor.  Yule was able to show that the process gave rise to a distribution with a power-law tail, but the details of his proof are, by today's standards, contorted and difficult, since the modern tools of stochastic process theory did not yet exist and he was forced to use more cumbersome methods of proof.

1925年，那时的Udny Yule是第一个对优先链接进行严谨考量的人，他用它来解释被子植物属中物种数量的幂律分布。为了纪念他，这个过程有时被称为“Yule过程”。Yule能够证明这个过程产生了一个带有幂律尾巴的分布，但是他的证明的细节，按照今天的标准，是曲折和晦涩的，因为现代的随机过程理论工具当时还不存在，他被迫使用更加繁琐的证明方法。

1925年，那时的Udny Yule是第一个对优先链接进行严谨考量的人，他用它来解释被子植物属中物种数量的幂律分布。<ref name=YulePhilTrans />为了纪念他，这个过程有时被称为“Yule过程”。Yule能够证明这个过程产生了一个带有幂律尾巴的分布，但是他的证明的细节，按照今天的标准，是曲折和晦涩的，因为现代的随机过程理论工具当时还不存在，他被迫使用更加繁琐的证明方法。

Most modern treatments of preferential attachment make use of the master equation method, whose use in this context was pioneered by Simon in 1955, in work on the distribution of sizes of cities and other phenomena.

Most modern treatments of preferential attachment make use of the master equation method, whose use in this context was pioneered by Simon in 1955, in work on the distribution of sizes of cities and other phenomena.

大多数现代优先链接的处理方法都使用了'''<font color="#ff8000">主方程方法 Master Equation Method</font>'''，这种方法在1955年由 Simon 首创，用于研究城市规模和其他现象的分布。

大多数现代优先链接的处理方法都使用了'''<font color="#ff8000">主方程方法 Master Equation Method</font>'''，这种方法在1955年由 Simon 首创，用于研究城市规模和其他现象的分布。<ref name=SimonBiomet />

The first application of preferential attachment to learned citations was given by Price in 1976.  (He referred to the process as a "cumulative advantage" process.)  His was also the first application of the process to the growth of a network, producing what would now be called a scale-free network.  It is in the context of network growth that the process is most frequently studied today.  Price also promoted preferential attachment as a possible explanation for power laws in many other phenomena, including Lotka's law of scientific productivity and Bradford's law of journal use.

The first application of preferential attachment to learned citations was given by Price in 1976.  (He referred to the process as a "cumulative advantage" process.)  His was also the first application of the process to the growth of a network, producing what would now be called a scale-free network.  It is in the context of network growth that the process is most frequently studied today.  Price also promoted preferential attachment as a possible explanation for power laws in many other phenomena, including Lotka's law of scientific productivity and Bradford's law of journal use.

普赖斯于1976年首次将优先链接应用于学术引文。(他把这个过程称为'''<font color="#ff8000">“优势累积” Cumulative Advantage</font>'''过程。)他也是第一个将这一过程应用于网络发展的人，他创造了现在所谓的'''<font color="#ff8000">无标度网络 Scale-Free Network</font>'''。正是在网络增长的背景下，这一过程在今天得到了最频繁的研究。普莱斯还将优先链接作为许多其他现象中幂定律的可能解释，包括洛特卡的科学生产力定律和布拉德福德的期刊使用定律。

普赖斯于1976年首次将优先链接应用于学术引文。<ref name=PriceJASIS />(他把这个过程称为'''<font color="#ff8000">“优势累积” Cumulative Advantage</font>'''过程。)他也是第一个将这一过程应用于网络发展的人，他创造了现在所谓的'''<font color="#ff8000">无标度网络 Scale-Free Network</font>'''。正是在网络增长的背景下，这一过程在今天得到了最频繁的研究。普莱斯还将优先链接作为许多其他现象中幂定律的可能解释，包括洛特卡的科学生产力定律和布拉德福德的期刊使用定律。

The application of preferential attachment to the growth of the World Wide Web was proposed by Barabási and Albert in 1999.

The application of preferential attachment to the growth of the World Wide Web was proposed by Barabási and Albert in 1999.

1999年，Barabási 和 Albert 提出了优先链接在万维网发展中的应用。

1999年，Barabási 和 Albert 提出了优先链接在万维网发展中的应用。<ref name=BAScience />