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| 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.
History
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
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| 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.
Characteristics
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.
History
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".
Definition
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.
Example
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.
History
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.
Examples
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
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| "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.
History
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.
Application
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
BONUS
 |
| 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
POST SCRIPT
Predicting collective online behavior
NOTE: the text of this blog consists of barely modified Wikipedia articles presented as actual blog
POST SCRIPT
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, phys.org
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
Physicists eye neural fly data, find formula for Zipf's law
August 2014, phys.org
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
