Sunday, February 17, 2013

Laws Meta-Physical

(aka) Rhizomatic Growth Structures

Bose–Einstein Condensation (network theory) à

Bose-Einstein condensate
A condensation phenomenon occurs when a distribution of a large number of elements in a large number of element classes becomes degenerate, i.e. instead of having an even distribution of elements in the classes, one class (or a few classes) become occupied by a finite fraction of all the elements of the system.

Condensation transitions occur in traffic jams, where long queues of cars are found, in wealth distribution models where a few people might have a finite fraction of all the wealth.

Ginestra Bianconi, graduate student with Prof. Albert-László Barabási, began investigating the fitness model, a model in which the network evolves with the "preferential attachment" mechanism but in addition, each node has an intrinsic quality or fitness that describe its ability to acquire new links. For example, in the world wide web each web page has a different content, in social networks different people might have different social skills, in airport networks each airport is connected to cities with unevenly distributed economic activity, etc. It was found that that under certain conditions, a single node could acquire most, if not all of the links in the network, resulting in the network analog of a Bose–Einstein condensate.
Bianconi, G.; Barabási, A.-L. (2001). "Bose–Einstein Condensation in Complex Networks." Phys. Rev. Lett. 86: 5632–35.

Connection with network theory
Addressing the dynamical properties of these nonequilibrium systems within the framework of equilibrium quantum gases predicts that the “first-mover-advantage,” “fit-get-rich(FGR),” and “winner-takes-all” phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks.
Bianconi, G.; Barabási, A.-L. (2001). "Bose–Einstein Condensation in Complex Networks." Phys. Rev. Lett. 86: 5632–35.
Bose-Einstein condensation in evolutionary models and ecological systems
Weiss V., Weiss H. (2003). The golden mean as clock cycle of brain waves. Chaos, Solitons and Fractals, 18, 643-652.

Fitness Model (network theory) à

scale invariant pyramids: Peter Bertok
In complex network theory, the fitness model is a model of the evolution of a network: how the links between nodes change over time depends on the fitness of nodes. Fitter nodes attract more links at the expense of less fit nodes.

The model is based on the idea of fitness, an inherent competitive factor that nodes may have, capable of affecting the network's evolution. According to this idea, the nodes' intrinsic ability to attract links in the network varies from node to node, the most efficient (or "fit") being able to gather more edges in the expense of others. In that sense, not all nodes are identical to each other, and they claim their degree increase according to the fitness they possess every time. The fitness factors of all the nodes composing the network may form a distribution characteristic of the system been studied.

Scale-Free Network à

Scale-free network sample
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.

Recent interest in scale-free networks started in 1999 with work by Albert-László Barabási and colleagues at the University of Notre Dame who mapped the topology of a portion of the World Wide Web,[2] finding that some nodes, which they called "hubs", had many more connections than others and that the network as a whole had a power-law distribution of the number of links connecting to a node.

Preferential attachment and the fitness model have been proposed as mechanisms to explain conjectured power law degree distributions in real networks.

This hierarchy allows for a fault tolerant behavior. If failures occur at random and the vast majority of nodes are those with small degree, the likelihood that a hub would be affected is almost negligible. Even if a hub-failure occurs, the network will generally not lose its connectedness, due to the remaining hubs. On the other hand, if we choose a few major hubs and take them out of the network, the network is turned into a set of rather isolated graphs. Thus, hubs are both a strength and a weakness of scale-free networks.

The random removal of even a large fraction of vertices impacts the overall connectedness of the network very little, suggesting that such topologies could be useful for security, while targeted attacks destroys the connectedness very quickly.

This model was originally discovered by Derek J. de Solla Price in 1965 under the term cumulative advantage, but did not reach popularity until Barabási rediscovered the results under its current name (Barabási–Albert model, or BA Model).
Barabási, Albert-László; Albert, Réka. (October 15, 1999). "Emergence of scaling in random networks". Science 286 (5439): 509–512.

Preferential Attachment à
aka The Network Effect

Preferential Attachment
A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. "Preferential attachment" is only the most recent of many names that have been given to such processes. They are also referred to under the names "Yule process", "cumulative advantage", "the rich get richer", and, less correctly, the "Matthew effect".

A preferential attachment process is a stochastic urn process, meaning a process in which discrete units of wealth, usually called "balls", are added in a random or partly random fashion to a set of objects or containers, usually called "urns". A preferential attachment process is an urn process in which additional balls are added continuously to the system and are distributed among the urns as an increasing function of the number of balls the urns 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 species is added to a new 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.

Preferential attachment is considered a possible candidate for, among other things, the distribution of the sizes of cities, the wealth of extremely wealthy individuals, the number of citations received by learned publications, and the number of links to pages on the World Wide Web.

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.
Price, D. J. de S. (1976). "A general theory of bibliometric and other cumulative advantage processes". J. Amer. Soc. Inform. Sci. 27 (5): 292–306.

Matthew Effect (sociology) à
aka "accumulated advantage"

The Matthew Effect was coined by Robert K. Merton to describe how eminent scientists get more credit than a comparatively unknown researcher, even if their work is similar, so that credit will usually be given to researchers who are already famous. Merton notes that "this pattern of recognition, skewed in favor of the established scientist, appears principally (i) in cases of collaboration and (ii) in cases of independent multiple discoveries made by scientists of distinctly different rank."

In the sociology of science, "Matthew effect" was a term coined by Robert K. Merton to describe how, among other things, eminent scientists will often get more credit than a comparatively unknown researcher, even if their work is similar; it also means that credit will usually be given to researchers who are already famous. For example, a prize will almost always be awarded to the most senior researcher involved in a project, even if all the work was done by a graduate student. This was later jokingly coined Stigler's law, with Stigler explicitly naming Merton as the true discoverer.

In his 2011 book The Better Angels of Our Nature: Why Violence Has Declined, cognitive psychologist Steven Pinker refers to the Matthew Effect in societies, whereby everything seems to go right in some, and wrong in others. He speculates in Chapter 9 that this could be the result of a positive feedback loop in which reckless behavior by some individuals creates a chaotic environment that encourages reckless behavior by others. He cites research showing that the more unstable the environment, the more steeply people discount the future, and thus the less forward-looking their behavior.
Merton, Robert K. (January 5, 1968). "The Matthew Effect in Science". Science 159.
Merton, Robert K. (1988). The Matthew Effect in Science, II: Cumulative advantage and the symbolism of intellectual property (PDF ). ISIS 79, 606–623.

Wealth Concentration à
"The rich get richer and the poor get poorer" is a catchphrase and proverb, frequently used (with variations in wording) in discussing economic inequality.
Wealth Concentration, also known as wealth condensation, is a process by which, in some conditions, newly created wealth tends to become concentrated in the possession of already-wealthy individuals or entities, a form of preferential attachment. Those who already hold wealth have the means to invest in new sources and structure, thus creating more wealth, or to otherwise leverage the accumulation of wealth, thus are the beneficiaries of the new wealth.

Zipf's Law à

zipf’s law
The most frequent word in a language, or in a book, or whatever, will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc.

zipf’s law
In the Brown University Standard Corpus of Present-Day American English, the word "the" is the most frequently occurring word, and by itself accounts for nearly 7% of all word occurrences (69,971 out of slightly over 1 million). True to Zipf's Law, the second-place word "of" accounts for slightly over 3.5% of words (36,411 occurrences), followed by "and" (28,852). Only 135 vocabulary items are needed to account for half the Brown Corpus.

Benford's Law à

Benford’s Law
In this distribution, the number 1 occurs as the first digit about 30% of the time, while larger numbers occur in that position less frequently, with larger numbers occurring less often: 9 as the first digit less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on a logarithmic scale.

This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

The discovery of Benford's law goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables (used at that time to perform calculations) the earlier pages (which contained numbers that started with 1) were much more worn than the other pages.

The phenomenon was again noted in 1938 by the physicist Frank Benford,[1] who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of 335 rivers, the sizes of 3259 US populations, 104 physical constants, 1800 molecular weights, 5000 entries from a mathematical handbook, 308 numbers contained in an issue of Readers' Digest, the street addresses of the first 342 persons listed in American Men of Science and 418 death rates. The total number of observations used in the paper was 20,229. This discovery was later named after Benford making it an example of Stigler's law.

Scale invariance
If there is a list of lengths, the distribution of numbers in the list may be generally similar regardless of whether all the lengths are expressed in metres, or feet, or inches, etc. For example, "1234 feet" and "1234 meters" are about equally likely to be in a list of lengths of randomly-chosen streets.

Accounting fraud detection
In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results.[8] Following this idea, Mark Nigrini showed that Benford's law could be used in forensic accounting and auditing as an indicator of accounting and expenses fraud.[9] In practice, applications of Benford's law for fraud detection routinely use more than the first digit.
-Mark J. Nigrini (May 1999). "I've Got Your Number". Journal of Accountancy.
Frank Benford (March 1938). "The law of anomalous numbers". Proceedings of the American Philosophical Society 78 (4): 551–572. JSTOR 984802.
Simon Newcomb (1881). "Note on the frequency of use of the different digits in natural numbers". American Journal of Mathematics (American Journal of Mathematics, Vol. 4, No. 1) 4 (1/4): 39–40.

Stigler's Law of Eponymy à
"No scientific discovery is named after its original discoverer." Stigler named the sociologist Robert K. Merton as the discoverer of "Stigler's law", consciously making "Stigler's law" exemplify itself.
Gieryn, T. F., ed. (1980). Science and social structure: a festschrift for Robert K. Merton. New York: NY Academy of Sciences. pp. 147–57.


A real-fake book about eponymy written by an author with noname FTW
While searching images for Stigler’s law, I found this book written and published by robots. It looked fishy; a quick search of the (unreal/non-human) author verified it.

Having read about these bot-generated books, I was very excited to sniff one out myself, (not that it requires any effort, just the knowledge that it exists), but the fact that a bot is writing about Stigler’s law is just funny in itself.

(The text of these books consists of unmodified Wikipedia articles sold as actual books.)
NOTE: the text of this blog consists of barely modified Wikipedia articles presented as actual blog

Marrying superconductors, lasers, and Bose-Einstein condensates

Chapman University Institute for Quantum Studies (IQS) member Yutaka Shikano, Ph.D., recently had research published in Scientific Reports. Superconductors are one of the most remarkable phenomena in physics, with amazing ...

Predicting collective online behavior

A new study shows that small websites, in terms of daily user flux based on number of clicks, have a disproportionally high impact when it comes to traffic generation and influence compared to larger websites.

Previous studies have analysed hyperlinks, while individual browsing records provide insight for understanding local surfing behaviour. However, they fail to provide information on more internet-wide collective browsing behaviour. Hence, to understand the complex interactions between websites, it is necessary to analyse the transportation of traffic, referred to as the flow of clickstreams between websites.

Physicists eye neural fly data, find formula for Zipf's law
August 2014,

mathematical models, which demonstrate how Zipf's law naturally arises when a sufficient number of units react to a hidden variable in a system.

"If a system has some hidden variable, and many units, such as 40 or 50 neurons, are adapted and responding to the variable, then Zipf's law will kick in."

"We showed mathematically that the system becomes Zipfian when you're recording the activity of many units, such as neurons, and all of the units are responding to the same variable".

Ilya Nemenman, biophysicist at Emory University and co-author

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