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Benford’s Law can detect malicious social bots | Golbeck | First Monday
Abstract: "Social bots are a growing presence and problem on social media. There is a burgeoning body of work on bot detection, often based in machine learning with a variety of sophisticated features. In this paper, we present a simple technique to detect bots: adherence with Benford’s Law. Benford’s Law states that, in naturally occurring systems, the frequency of numbers first digits is not evenly distributed. Numbers beginning with a 1 occur roughly 30 percent of the time, and are six times more common than numbers beginning with a 9. In earlier work, we established that Benford’s Law holds for social connections across online social networks. In this paper, we show that this principle can be used to detect bots because they violate the expected distribution. In three studies — an analysis of a large Russian botnet we discovered, and studies of purchased retweets on Twitter and purchased likes on Facebook — we show that bots’ social patterns consistently violate Benford’s Law while legitimate users follow it closely. Our results offer a computationally efficient new tool for bot detection. There are also broader implications for understanding fraudulent online behavior. Benford’s Law is present in many aspects of online social interactions, and looking for violations of the distribution holds promise for a range of new applications."
bots  socialmedia  statistics  maths  FirstMonday 
10 weeks ago by pierredv
History, Differential Equations, and the Problem of Narration on JSTOR, Donald N. McCloskey, 1991
Donald N. McCloskey
History and Theory, Vol. 30, No. 1 (Feb., 1991), pp. 21-36
Stable URL:


… engineers specialize in metaphors and historians in stories. In the abstract it is a matter of definitions. Take the essence of the metaphor to be comparison and the essence of the story to be time.

The engineer and historian do not deal in mere comparison or mere time, no more than poets or novelists do. Aimless comparison is bad poetry and bad engineering; one damned thing after another is bad fiction and bad history.

Like the terms of most human histories, most solutions of differential equations in this explicit form (called "analytic solutions") cannot be achieved mechanically. They have to be guessed at, then confirmed by showing they correspond with the original equations, which is to say with the partially thematized chronologies that we call history. Even the ones that do not have analytic solutions often have approximate solutions in terms of what are called, alarmingly, "infinite series." The successive terms of such series are approximate themes. For instance, the large first term in an infinite series of themes for World War I might be "God favors the bigger battalions," to which might be added the somewhat less important second term (" . . . and the better generals"), to which might be added the third (" . . . and the British Empire"), and so on, out to the limit of the historian's or the engineer's need for thematization. (The engineer uses the thematization to characterize and predict, the historian to characterize and explain, but otherwise they are doing much the same job: one is predicting, the other postdicting.)

The analytic solutions correspond to simply predictable histories, that is, histories that can be reexpressed as equations. The differential equations embody what we think we know about societies as theory, such as a Marxist theory. The solution then characterizes a particular historical path. . . . Such talk undermines the claim that natural science and historical science have two separate modes of apprehension. The separation seems less consequential if it is viewed merely as the metaphor as against the story, and if in good metaphors and good stories the two are linked by a differential equation. The old question - Clio, Science or Muse? - loses its gripping interest if sciences use stories and art uses number.

The commonest theme of battle history, the horseshoe nail, is a case of a non- linear differential equation: . . . Battle history is not held in high regard by historians precisely because it so obviously depends on tiny chances of this sort. . . . But the disdain for assigning large events small causes is not rational in a world partly nonlinear.

But the attraction of the chaotic is also the attraction of magic. The accident has the power of magic, a childish omnipotence of thought in which I can change the world with a word. . . . Tiny errors in a magical ceremony can make it go wrong. "If the Hindu magicians are to be believed, some of their rites could be practiced successfully only once every forty-five years." Naturally: if magic could be done on any day, in any place, it would not have the scarcity that protects its claim of efficacy. It would merely be engineering.

Chaos pleases us, then, by reintroducing a sense of magic, a sense of many possibilities.

. . . The Dogma of Large-Large. Large results, it says, must have large causes.

The butterfly can take flight either in the parameters (that is, in the confidence about the model imposed) or in the initial conditions (that is, in the confidence about the observations of the world's condition). Both yield large differences out of small differences. Only unreasonable dogmatism about the model or un- reasonable dogmatism about acuity can restore one's confidence in the Dogma of Large-Large.

What we can do is look for times that seem chaotic and be forewarned. That is what engineers do.

One does not avoid nonlinearities by not knowing what they are called. When success breeds success, when variables feed back into themselves, we have an exciting story to tell, but unless we know its metaphors already we have no way to tell it.
history  narration  stories  engineering  maths 
may 2019 by pierredv
Mathematics of the Discrete Fourier Transform (DFT) with audio applications, Second Edition, Julius O. Smith III
Mathematics of the Discrete Fourier Transform (DFT) with audio applications
Second Edition

Julius O. Smith III
textbooks  DSP  signal-processing  maths 
october 2018 by pierredv
Fourier’s transformational thinking - Nature Mar 2018
Via Dale Hatfield

"The mathematics of Joseph Fourier, born 250 years ago this week, shows the value of intellectual boldness."
physics  history  profile  NatureJournal  maths 
march 2018 by pierredv
‘Wavelet revolution’ pioneer scoops top maths award : Nature News & Comment - Mar 2017
"French mathematician Yves Meyer has won the 2017 Abel Prize for his “pivotal role” in establishing the theory of wavelets — data-analysis tools used in everything from pinpointing gravitational waves to compressing digital films."
physics  NatureJournal  maths 
march 2018 by pierredv
The geometry that could reveal the true nature of space-time | New Scientist issue 3136, 29 Jul 2017
"The discovery of an exquisite geometric structure is forcing a radical rethink of reality, and could clear the way to a quantum theory of gravity"

[Andrew Hodges, one of Penrose’s colleagues at Oxford] "showed that the various terms used in the BCFW method could be interpreted as the volumes of tetrahedrons in twistor space, and that summing them up led to the volume of a polyhedron."

"So why invoke virtual particles at all? ... The first is that dealing with them rather than with fields makes the maths more tractable. The other great advantage is that they help physicists visualise everything as the well-defined interactions between point-like particles, as opposed to the hazy goings-on between particles and fields. This fits nicely with the intuitive principle of locality, which holds that only things in the same spot in space and time can interact. Finally, the technique also helps enforce the principle of unitarity, which says that the probability of all outcomes should add up to 1."

Gluon interactions seemed to complex, but "In 1986, Stephen Parke and Tomasz Taylor from Fermilab near Batavia, Illinois, used Feynman diagrams and supercomputers to calculate the likelihoods of different outcomes for interactions involving a total of six gluons. A few months later, they made an educated guess at a one-line formula to calculate the same thing. It was spot on. More than 200 Feynman diagrams and many pages of algebra had been reduced to one equation, and the researchers had no idea why."

"In 2005, Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten [BCFW] were able to calculate scattering amplitudes without recourse to a single virtual particle and derived the equation Parke and Taylor had intuited for that six-gluon interaction"

[Nima Arkani-Hamed and his team at IAS] "arrived at a mind-boggling conclusion: the scattering amplitude calculated with the BCFW technique corresponds beautifully to the volume of a new mathematical object. They gave a name to this multi-dimensional concatenation of polyhedrons: the amplituhedron."

"It may transform physics, too ... because the amplituhedron does not embody unitarity and locality, those core principles baked into reality as described by Feynman diagrams. ... If so, locality is not a fundamental feature of space-time but an emergent one."
NewScientist  geometry  physics  gravity  field-theory  quantum-mechanics  twistors  Roger-Penrose  Richard-Feynman  Ed-Witten  maths 
december 2017 by pierredv
Early Computer Programming - The British Library
"Ada Lovelace (1815-52) was the daughter of Lord Byron. She was educated to be a mathematician because her mother feared she might turn out to be a poet like her father."
poetry  people  maths 
july 2017 by pierredv
Mathematicians shocked to find pattern in 'random' prime numbers | New Scientist - April 2016
"Although whether a number is prime or not is pre-determined, mathematicians don’t have a way to predict which numbers are prime, and so tend to treat them as if they occur randomly. Now Kannan Soundararajan and Robert Lemke Oliver of Stanford University in California have discovered that isn’t quite right."
"Just as Einstein’s theory of relativity is an advance on Newton’s theory of gravity, the Hardy-Littlewood conjecture is essentially a more complicated version of the assumption that primes are random – and this latest find demonstrates how the two assumptions differ. “Mathematicians go around assuming primes are random, and 99 per cent of the time this is correct, but you need to remember the 1 per cent of the time it isn’t,” says Maynard. The pair used Hardy and Littlewood’s work to show that the groupings given by the conjecture are responsible for introducing this last-digit pattern, as they place restrictions on where the last digit of each prime can fall. What’s more, as the primes stretch to infinity, they do eventually shake off the pattern and give the random distribution mathematicians are used to expecting."
NewScientist  primes  maths 
august 2016 by pierredv
The play X will have you clock-watching - but in a good way | New Scientist - April 2016
"X, which opened at London’s Royal Court Theatre on 30 March, is McDowall’s most ambitious work yet. It is a deeply human story of life and loss played out across unthinkable distances, and raises harrowing questions about the limits of cognition and the structural weaknesses of the human mind."
"One of the play’s recurrent themes is that mathematics – and algebra in particular – is not really our friend. Maths can be unearthed from ancient civilisations, as hard and undeniable as a splinter of pottery. That is what makes it sacred. It is also precisely what makes maths horrible: it goes where we can’t. It handles centuries as easily as it handles hours, and navigates between planets as easily as it crosses oceans.

And we can’t. We are physical beings who operate at a certain scale. Our smallness in a very big universe is truly an a priori condition: it is not up for negotiation."
NewScientist  reviews  theater  maths 
august 2016 by pierredv
The maddeningly magical maths of John Dee - New Scientist Feb 2016
Discussion of "Scholar, Courtier, Magician: The lost library of John Dee" - showing at the Royal College of Physicians, London, until 29 July 2016.

Bits from Dee's preface to "The Elements of Geometrie", published in 1570 by Henry Billingsley, are fascinating.

"some of the suspicion aroused by Nicolaus Copernicus’s De revolutionibus in 1543 came not from his heliocentric theory of the solar system, but from the fact that he used maths to deduce what he could not directly see"

Also deep suspicion of cryptography isn't new: "And maths really did have connections with the occult. Numerology was important to the Jewish mystical tradition called the Kabbalah, which Dee studied closely. Codes and cryptography were discussed in Steganographia (c. 1499) by the German abbot Trithemius, who was suspected of diabolical wizardry; it was this book that Dee examined to understand angelic communication."
science  maths  scientific-method  exhibition  history  cryptography 
april 2016 by pierredv
The Relation between Mathematics and Physics by Paul Adrien Maurice Dirac
Lecture delivered on presentation of the JAMES SCOTT prize, February 6, 1939
Published in: Proceedings of the Royal Society (Edinburgh) Vol. 59, 1938-39, Part II pp. 122-129
physics  beauty  Paul-Dirac  maths 
march 2016 by pierredv
Matrix villain spawns 177,000 ways to knot a tie - physics-math - 07 February 2014 - New Scientist
"In 1999, Thomas Fink and Yong Mao of the University of Cambridge published a mathematical language describing tie knots in the journal Nature. The pair used an existing tool from logic – known as formal language theory – to express the basic rules of tying a neck tie as a series of symbols. This included things like the placement of the tie, the direction of the fold and the need to end in a final tuck. They used their tie language to show that only 85 knots were possible. Now mathematician Mikael Vejdemo-Johansson of the KTH Royal Institute of Technology in Stockholm, Sweden, has vastly broadened the tie landscape."
maths  topology  video  tie  NewScientist 
april 2014 by pierredv
The Paradox of the Proof | Project Wordsworth
Via Henry Yuen. Quote of O'Niel ("mathbabe"_ “You don’t get to say you’ve proved something if you haven’t explained it,” she says. “A proof is a social construct. If the community doesn’t understand it, you haven’t done your job.” From piece: "The community works together; they are not cut-throat or competitive. Colleagues check each other’s work, spending hours upon hours verifying that a peer got it right. This behavior is not just altruistic, but also necessary: unlike in medical science, where you know you’re right if the patient is cured, or in engineering, where the rocket either launches or it doesn’t, theoretical math, better known as “pure” math, has no physical, visible standard. It is entirely based on logic. To know you’re right means you need someone else, preferably many other people, to walk in your footsteps and confirm that every step was made on solid ground. A proof in a vacuum is no proof at all."
stories  community  proof  meaning  maths 
may 2013 by pierredv
Do you need to know math for doing great science? | The Curious Wavefunction, Scientific American Blog Network
"Writing in the Wall Street Journal, biologist E. O. Wilson asks if math is necessary for doing great science. At first glance the question seems rather pointless and the answer trivial; we can easily name dozens of Nobel Prize winners whose work was not mathematical at all. Most top chemists and biomedical researchers have little use for mathematics per se, except in terms of using statistical software or basic calculus. The history of science is filled with scientists like Darwin, Lavoisier and Linnaeus who were poor mathematicians but who revolutionized their fields. But Wilson seems to be approaching this question from two different perspectives and by and large I agree with both of them. The first perspective is from the point of view of students and the second is from the point of view of research scientists. Wilson contends that many students who want to become scientists are put off when they are told that they need to know mathematics well to become great scientists."
research  maths 
april 2013 by pierredv
What Tau Sounds Like - YouTube
Musician interprets the mathematical constant Tau to 126 decimal places.
music  maths 
march 2013 by pierredv
A Mathematical Approach to Safeguarding Private Data | Simons Foundation
Great survey of differential privacy, with good quotes from Frank McSherry:
“We’ve learned that human intuition about what is private is not especially good”
"Differential privacy assumes that the adversary is all-powerful . . Differential privacy is future-proofed"
“Privacy is a nonrenewable resource. . . Once it gets consumed, it is gone.”

Definition: "Differential privacy focuses on information-releasing algorithms, which take in questions about a database and spit out answers — not exact answers, but answers that have been randomly altered in a prescribed way. When the same question is asked of a pair of databases (A and B) that differ only with regard to a single individual (Person X), the algorithm should spit out essentially the same answers."

Also discusses privacy budgets, PINQ programming language
programming-languages  differential-privacy  *  CynthiaDwork  Microsoft  privacy  x:SimonsFoundation  quotations  maths 
december 2012 by pierredv
A Faster Fast Fourier Transform - IEEE Spectrum March 2012
"The newest MIT algorithm, which is described in a soon-to-be-published paper, beats the traditional FFT so long as the number of frequency components present is a single-digit percentage of the number of samples you take of the signal. It works for any signal, but it works faster than the FFT only under those conditions"
science  technology  FFT  via:stevecrowley  maths 
march 2012 by pierredv
Quantum minds: Why we think like quarks - life - 05 September 2011 - New Scientist
Strapline: "The fuzziness and weird logic of the way particles behave applies surprisingly well to how humans think" Application of Hilbert space theory ("quantum logic") to behavior "We make systematic errors when reasoning with probabilities, for example. Physicist Diederik Aerts of the Free University of Brussels, Belgium, has shown that these errors actually make sense within a wider logic based on quantum mathematics. The same logic also seems to fit naturally with how people link concepts together, often on the basis of loose associations and blurred boundaries. That means search algorithms based on quantum logic could uncover meanings in masses of text more efficiently than classical algorithms." Cites research by Aerts; Tversky & Shafir; Busemeyer & Pothos; Widdows, Cohen; etc.
physics  behavior  maths  NewScientist  quarks  quantum-mechanics 
november 2011 by pierredv
Pi's nemesis: Mathematics is better with tau - physics-math - 12 January 2011 - New Scientist
"It's time to kill off pi, says physicist Michael Hartl, who believes that an alternative mathematical constant will do its job better"
NewScientist  humor  interviews  maths 
january 2011 by pierredv
Benford's Law And A Theory of Everything - MIT Technology Review
"Benford Law seems to apply only to certain types of data. Physicists have found that it crops up in an amazing variety of data sets. Here are just a few: the areas of lakes, the lengths of rivers, the physical constants, stock market indices, file sizes in a personal computer and so on."

However, there are many data sets that do not follow Benford's law, such as lottery and telephone numbers.

What's the difference between these data sets that makes Benford's law apply or not? It's hard to escape the feeling that something deeper must be going on.
physics  statistics  patterns  maths 
january 2011 by pierredv
The Mathematician And The Pig -
Why math skills aren't so important
by Lionel Tiger, the Charles Darwin Professor of Anthropology at Rutgers University
"How a country chooses its elites reflects its core values and assumptions about the nature of human social life. The emphasis of 50% on math skills may be appropriate for a tiny group of professional mathematicians, but for the rest of us, sophisticated higher math is one of the least useful human skills."
maths  culture  via:forbes  *** 
september 2008 by pierredv
Fermat's Last Theorem (1996)
45 min - documentary on Andrew Wiles
video  NewScientist  ***  maths 
june 2008 by pierredv
Ron Eglash Home Page
via TED research topics: African Fractals Native American Cybernetics Culturally Situated Design Tools Community Informatics Communication Studies Race/Ethnicity in Science and Technology Appropriating Technology: vernacular science and social power
profile  maths  culture  Africa 
january 2008 by pierredv
'Cool Cash' card confusion - News - Manchester Evening News
Confusion about whether -6 is higher or lower than -8
"The 23-year-old, who said she had left school without a maths GCSE, said: "On one of my cards it said I had to find temperatures lower than -8. The numbers I uncovered were -6 and -7 so I thought I h
humor  maths  education  via:GMSV 
november 2007 by pierredv
Arithmetic Is Hard--To Get Right
discussion of discrete arithmetic, in the context of the Excel multiplication bug that just came to light (9/26/2007)
programming  maths  bugs 
september 2007 by pierredv
Derek's Virtual Slide Rule Gallery
gallery of clickable simulated slide rules
engineering  retro  design  science  maths 
july 2007 by pierredv
Last doubts removed about the proof of the Four Color Theorem
Keith Devlin
Covers discussion of Gonthier's use of a computer "mathematical assistent" to help mathematicians with proofs
maths  computing 
june 2007 by pierredv
Nonlinearity - Wikipedia, the free encyclopedia
"In mathematics, nonlinear systems represent systems whose behavior is not expressible as a sum of the behaviors of its descriptors. In particular, the behavior of nonlinear systems is not subject to the principle of superposition, as linear systems are.
hardproblems  maths 
april 2007 by pierredv
Gregory Chaitin: The Omega Man -- New Scientist
Feature on Gregory Chaitin by Marcus Chown.
"Chaitin has shown that there are an infinite number of mathematical facts but, for the most part, they are unrelated to each other and impossible to tie together with unifying theorems. If mathematicians find
maths  science  hardproblems 
december 2006 by pierredv
Not just a pretty equation - opinion - 25 November 2006 - New Scientist
Review of "Mathematics and common sense" by Philip Davis (John Ball). "This reflects the principal theme of the book: the creative tension that Davis sees between the things in mathematics that are obvious and intuitive - common sense - and the things tha
maths  hardproblems 
december 2006 by pierredv
Easy Mental Multiplication Trick Video
How to transform a multiplication into addition through the drawing of a stool. It works with any numbers if you keep the right partition.
maths  video 
november 2006 by pierredv
YouTube - look around you maths
English straighfaced parody of science features for kids
video  maths 
june 2006 by pierredv
incl formulas (without derivation) for number of corners, edges, squares, etc.
march 2006 by pierredv
The Impact of Emerging Technologies: Newer Math? - Technology Review
A new high-school mathematics might someday model complex adaptive systems.
By Rodney Brooks
maths  complexity 
march 2006 by pierredv

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