alignment problem

Popularized by the 2020 book The Alignment Problem by Brian Christian.

As [Brian] Christian notes, the alignment problem bears a real resemblance to parenting: “The story of human civilization has always been about how to instill values in strange, alien, human-level intelligences who will inevitably inherit the reins of society from us—namely, our kids.”

2022 March 1, Rob Toews, “7 Must-Read Books About Artificial Intelligence”, in Forbes, New York, N.Y.: Forbes Media, →ISSN, →OCLC, archived from the original on 2022-08-31:

Properly defining and solving the alignment problem won’t be easy; it will require us to develop a broad, scientifically based theory of intelligence.

2022 December 13, Melanie Mitchell, “What Does It Mean to Align AI With Human Values?”, in Quanta Magazine, New York, N.Y.: Simons Foundation, →ISSN, →OCLC, archived from the original on 2023-03-15:

For years, AI ethicists have worried about this so-called alignment problem. In short: How do we ensure that the AI we build, which might very well be significantly smarter than any person who has ever lived, is aligned with the interests of its creators and of the human race? An unaligned superintelligent AI could be quite a problem.

2023 February 27, Derek Thompson, “The AI Disaster Scenario”, in The Atlantic, Washington, D.C.: The Atlantic Monthly Group, →ISSN, →OCLC, archived from the original on 2023-03-22:

artificial intelligence
artificial intelligence#Noun

(artificial intelligence) The problem of how to create a superintelligent artificial intelligence whose values would align with the interests of humankind.

AI alignment#The alignment problem
Brian Christian
The Alignment Problem


polygon-circle graph

en-noun

polygon-circle graph (plural polygon-circle graphs)

A common generalization of these two [circle graphs and circular arc graphs] are polygon-circle graphs, intersection graphs of convex polygons inscribed to the circle. This class was first suggested by M. Fellows [personal communication with the first author] in 1988, when it was pointed out that this class of graphs is closed under taking induced minors.

2004, Jan Kratochvíl, Martin Pergel, “Two Results on Intersection Graphs of Polygons”, in Giuseppe Liotta, editor, GD 2003 International Symposium on Graph Drawing (Lecture Notes in Computer Science), volume 2912, Springer-Verlag, →DOI, →ISBN, page 60:

(graph theory) A graph (set of connected points) in which each vertex corresponds to a convex polygon circumscribed in a common circle, and in which (graph) vertices are adjacent iff their corresponding polygons intersect geometrically.


plug into

en-verb

plug into (third-person singular simple present plugs into, present participle plugging into, simple past and past participle plugged into)

plugs into (present singular third-person)
plugging into (participle present)
plugged into (participle past)
plugged into (past)

If you know two sides of a right triangle, you can find the third by plugging them into the Pythagorean Theorem.

(idiomatic, mathematics) To replace a variable with a number in order to solve an equation.


microlife

en-noun

microlife (countable and uncountable, plural microlives)

Coordinate term: micromort

If you have unhealthy habits, it costs you microlives. If you smoke, each cigarette reduces your life expectancy on average by around 15 minutes, so two cigarettes loses you a microlife.

2012 February 16, David Spiegelhalter, “Microlives: A lesson in risk taking”, in BBC Future:

(countable) A unit of risk representing half an hour change of life expectancy.


rank-deficient

en-adj

rank-deficient (comparative more rank-deficient, superlative most rank-deficient)

more rank-deficient (comparative)
most rank-deficient (superlative)

(mathematics, linear algebra, of a matrix) Not having full rank; having a rank (dimension) less than the number of columns and the number of rows.


full rank

full rank (comparative more full rank, superlative most full rank)

more full rank (comparative)
most full rank (superlative)

(mathematics, linear algebra, of a matrix) Having the highest possible rank for its size; having a rank (dimension) equal to the number of columns or the number of rows.


complex conjugate root theorem

(mathematics, complex analysis) The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root.


ronnagram

The Earth weighs about six ronnagrams.

The arrival of the new prefixes means the Earth can now be said to weigh six ronnagrams, and Jupiter about two quettagrams.

2022 November 18, Ian Sample, “Earth weighs in at six ronnagrams as new prefixes picked for big and small”, in The Guardian:

(metrology) An SI unit of mass equal to 10²⁷ grams. Symbol: Rg


quesitive

(mathematics, obsolete) Of or relating to an unknown quantity.


hexahectaenneacontakaiheptagon

Analysable as hexahecta- (“six hundred”) (from hexa- + hect(a)-) + enneaconta- (“ninety”) (from ennea- + the common element in Ancient Greek ἑξήκοντα (hexḗkonta, “sixty”), τεσσαράκοντα (tessarákonta, “forty”), etc.) + Ancient Greek καί (kaí, “and”) + hepta- (“seven”) + -gon.
Coined humorously to describe the shape of the US state of Colorado.

der

Colorado is actually a hexahectaenneacontakaiheptagon, meaning it has 697 sides, according to a 2018 bigthink.com article and Kutztown University's math whizzes who create names for polygons.

2019 October 16, James Burky, “Rectangle state? Nope. Colorado has 697 sides, not four.”, in The Denver Post, archived from the original on 2023-01-08:

A study in 2018 suggested that as a result of the challenges of surveying in the nineteenth century, Colorado has no fewer than 697 sides, technically making it a "hexahectaenneacontakaiheptagon."

2020, Derek Everett, Colorado Day by Day, Boulder, CO: University Press of Colorado, →ISBN, page 212:

The state of Colorado may look like a rectangle (four straight sides, four right angles) but it actually has 697 sides, making it a hexahectaenneacontakaiheptagon.

2020, Bathroom Readers' Institute, Uncle John's Greatest Know on Earth Bathroom Reader, San Diego, CA: Portable Press, →ISBN:


pancake theorem

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ham sandwich theorem
ham sandwich theorem

(mathematics) The two-dimensional counterpart of the ham sandwich theorem.


semidisk

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biquadrated

2 biquadrated is equal to 16.

(mathematics) Raised to the fourth power.


Hausdorff gap

Named after German mathematician Felix Hausdorff (1868–1942), who published proof of the first example in 1909.

The existence of Hausdorff gaps shows that the partially ordered set of possible growth rates of sequences is not complete.

Of course, Hausdorff did not talk of models of set theory or prove absoluteness results. He gave a direct construction in ZFC of what is now called a Hausdorff gap and proved properties 1 through 4 for his construction. The notion of a Hausdorff gap and the proof that Hausdorff gaps are indestructible under cardinal preserving extensions (property 5 above) are due to Kunen (unpublished).

1995, Robert M. Solovay, “*1970 [Godel's ontological proof]”, in Kurt Gödel, edited by Solomon Feferman, John W. Dawson Jr., Warren Goldfarb, Charles Parsons, and Robert M. Solovay, Kurt Gödel: Collected Works: Volume III, Oxford University Press, page 419:

Let #92;langle#92;langlea#95;#92;epsilon#58;#92;epsilonlt;#92;omega#95;1#92;rangle#92;langleb#95;#92;epsilon#58;#92;epsilonlt;#92;omega#95;1#92;rangle#92;rangle be a Hausdorff gap.

1997, Winfried Just, Martin Weese, Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician, American Mathematical Society, page 118:

2013, Ilijas Farah, Eric Wofsey, 3: Set theory and operator algebras, James Cummings, Ernest Schimmerling (editors), Appalachian Set Theory: 2006-2012, London Mathematical Society, Cambridge University Press, page 101,
This family is one of the instances of incompactness of ω₁ that are provable in ZFC, along with Hausdorff gaps, special Aronszajn trees, or nontrivial coherent families of partial functions.

(set theory, order theory) A pair of collections of integer sequences such that there is no integer sequence lying between the two.


Borůvka's algorithm

(graph theory) A greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected.


Tarjan's algorithm

strongly connected component
strongly connected component

(graph theory) An algorithm for finding the strongly connected components (SCCs) of a directed (connected) graph by using the depth-first search function.


gyrobicupola

(mathematics) A bicupola in which the bases have the opposite orientation.


Milü

(mathematics) An approximation of pi: 355/113.


coshine

Should a shine or coshine be wanted which is not in the table, advantage may be taken of the differential of cosh x being sinh x, and vice versa. Thus, sinh x and cosh x being known, the shine or coshine of x + y, y being small compared to x, may be calculated from these relationships—[…]

1931, Charles George Watson, Sags and Tensions in Overhead Lines, London: Isaac Pitman & Sons, →OCLC, page 135:

Considering equation (8) in which ϵ = −1 we have a similar situation to our previous analysis in which the hyperbolic functions replace the trigonometric ones. However, this leads to significant changes in the results, e.g., if in equation (18) the cosines are replaced by coshines the equation has no solutions since coshines are always greater than or equal to one.

1984, D. E. Hodgkinson, “Empty space-times of embedding class two”, in General Relativity and Gravitation, volume 16, number 6, Springer, →ISSN, page 574:

In (4) the function cos{h} denotes that either cosine or coshine functions are used depending upon whether the third charateristic^([sic]) root is real or imaginary.

1996, L. N. McCartney, “Stress transfer mechanics for angle-ply laminates”, in ECCM-7: Seventh European Conference on Composite Materials, volume 2, pages 236–237:

hyperbolic cosine
hyperbolic cosine#English

(uncommon) Synonym of hyperbolic cosine.


cothangent

To see this let us expand the cothangent on the right-hand side of equation (26) in a power series to obtain […]

1971, J. Hubbard, “Spin-correlation functions in the paramagnetic phase of a Heisenberg ferromagnet”, in Journal of Physics C, volume 4, number 1, IOP Publishing, →ISSN, page 58:

While in the non-drifted case a generic h-slope not covering the origin behaves in proximity of its extremes as a 3D Bessel process, in the drifted case it behaves as a process with a cothangent drift, satisfying the SDE […]

2009, Alessandra Faggionato, “The alternating marked point process of h-slopes of drifted Brownian motion”, in Stochastic Processes and Their Applications, volume 119, number 6, Elsevier, →ISSN, page 1766:

hyperbolic cotangent
hyperbolic cotangent#English

(mathematics, uncommon) Synonym of hyperbolic cotangent.


pregroupoid

This implies that the so-called internal Galois pregroupoid of an extension is an internal groupoid..

2015, Marino Gran, Diana Rodelo, “Beck-Chevalley condition and Goursat categories”, in arXiv:

(category theory) A category together with its inversion.


decision theory

en-noun

decision theory (plural decision theories)

Info-gap decision theory is based on quantitative models and provides numerical decision-support assessments.

2006, Yakov Ben-Haim, Info-Gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Elsevier, →ISBN, page 3:

Decision theory gives a concise framework for making decisions based on models. Its components are a state space forming the range of a set of variables, alternatives or potential actions, and constraints on the decision space a set of consequences of actions, and a preference functional encoding and optimality criterion, involving the costs and value of extra information.

2014, Giacomo Della Riccia et al., editors, Planning Based on Decision Theory, Springer, →ISBN:

A branch of applied probability theory concerned with the theory of decision making based on models describing probabilities, actions, constraints, and preferences.


kaleidocycle

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(geometry) A flexible polyhedron connecting six tetrahedra (or disphenoids) on opposite edges into a cycle.


Lemoine point

The French mathematician Émile Lemoine proved the existence of such points in 1873.

(geometry) The intersection of the three symmedians of a triangle.


spherical triangle

spherical triangle (plural spherical triangles)

If the three sides of a spherical triangle be each of them equal to a quadrant, the polar triangle will coincide with it; for each of the angular points will be the pole of the side opposite to it.

1830, Pierce Morton, Geometry, Plane, Solid, and Spherical, in Six Books, Baldwin and Craddock, page 189:

570. Theorem. The sum of the sides of a spherical triangle may be anything between 0 and a circumference.

1876, Edward Olney, A Treatise on Special Or Elementary Geometry, Sheldon & Company, page 220:

1893, Crossley William Crosby Barlow, George Hartley Bryan, Elementary Mathematical Astronomy, W. B. Clive, page v,
A spherical triangle, like a plane triangle, has six parts, viz., its three sides and its three angles. The sides are generally measured by the angles they subtend, so that the six parts are all expressed as angles.
Any three parts suffice to determine a spherical triangle, but there are certain "ambiguous cases" when the problem admits of more than one solution. The formulæ required in solving spherical triangles form the subject of Spherical Trigonometry, and are in every case different from the analogous formulæ in Plane Trigonometry. There is this further difference, that a spherical triangle is completely determined if its three angles are given.

The angles in a spherical triangle do not have to add up to 180 degrees. It is possible for a spherical triangle to have 3 right angles.

2012, Daniel Zwillinger, CRC Standard Mathematical Tables and Formulae, 32nd edition, Taylor & Francis (CRC Press / Chapman & Hall), page 218:

(geometry, spherical geometry) A triangle, described on the surface of the sphere, whose each side is an arc of some great circle.

Kugeldreieck

Triangle on the surface of a sphere, whose sides are arcs of great circles


Ritz series

(mathematics) A generalization of a Fourier series extended to situations in which a displacement field has an arbitrary time dependence while still maintaining its spatial periodicity.


quasisymmetry

quasisymmetry (countable and uncountable, plural quasisymmetries)

(mathematics) A mapping that preserves shape but allows size to change in a well-defined manner.


subchord

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quantuplicity

quantuplicity (countable and uncountable, plural quantuplicities)

(mathematics, obsolete) Relative magnitude.


bilimit

(category theory) A generalization of the concept of a limit that is an equivalence class rather than a unique value.


convolvability

(mathematics) The property of being convolvable.


Blum integer

(mathematics) A type of mathematical sequence of integers that is describing a natural number n without an imaginary part which differs from the Gaussian integer, but the integer sequence is following correctly only if n = p × q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4.


awqiyyah

From Arabic أُوقِيَّة (ʔūqiyya). Doublet of ounce, inch, uncia, ouguiya, and oka.

doublet

An Egyptian unit of weight equivalent to about 37 grams (1.3 oz.)


dekeract

(mathematics) A ten-dimensional hypercube


omegath

(set theory, rare) In the position known as omega (a transfinite ordinal number referring to the next position after ordering a countably infinite set).


covado

From Portuguese côvado, from Old Galician-Portuguese côbedo, from Latin cubitum (“cubit”). Doublet of cubit and codo.

(historical, measure) A traditional Portuguese unit of length, usually about equal to 0.6 meters and approximating the length of a forearm and hand.


eigenbundle

(mathematics) Given a section s of an endomorphism bundle Hom(E, E) and a function f: X → R, an eigenbundle is the result of taking the fiber over a point x ∈ X to be the f(x)-eigenspace of the linear map s(x): Eₓ → Eₓ.


selamim

(historical) Alternative form of celamim


celamim

From Portuguese celamim, from Andalusian Arabic, from Arabic ثُمُنِ (ṯumuni, “of one-eighth”). Doublet of tomin and azumbre.

(historical) A traditional Portuguese unit of dry measure, equivalent to 0.4–0.6 L in different 19th-century contexts.


escropulo

Unadapted borrowing from Portuguese escrópulo, from Latin scrūpulus (“scruple, nagging doubt, 1/24 uncia”), from scrūpus (“sharp stone, anxiety”) + -ulus (“-ule: forming diminutives”). Doublet of scruple and escrupulo.

der

(historical) A traditional Portuguese unit of mass, equivalent to about 1.2 g.


arratel

From Portuguese arrátel, from Andalusian Arabic الرَطْل (“rottol”), from Arabic الرَطْل (ar-raṭl), from Aramaic רִיטְלָא / ܪܺܝܛܠܳܐ (rīṭlā), variant of לִיטְרָא / ܠܺܝܛܪܳܐ (līṭrā), from Ancient Greek λίτρα (lítra, “libra, Roman pound”). Doublet of libra, livre, libbra, liter, and rottol.

Aramaic רִיטְלָא

doublet

(historical) A traditional Portuguese unit of mass, usually equivalent to 459 g.


quintalejo

From Portuguese quintalejo, from quintal (“Portuguese hundredweight”) + -ejo (“-cule: forming diminutives”).

(historical) A traditional Portuguese unit of mass, usually equivalent to 29.4 kg.


eigenelement

(mathematics) A nonzero element m of a semimodule M, such that there exists an endomorphism A on M and a real number r (a corresponding eigenvalue) for which the image of m under A is equal to the product of r times m; i.e. mA=rm.


eigensection

(algebra) A homogenous section whose associated Eulerian family diagonalizes a given element of a Lie algebra.


escrupulo

Unadapted borrowing from Spanish escrúpulo, from Latin scrūpulus (“scruple, nagging doubt, ¹⁄₂₄ uncia”), from scrūpus (“sharp stone, anxiety”) + -ulus (“-ule: forming diminutives”). Doublet of scruple and escropulo.

der

scruple, nagging doubt, <small>¹<big>⁄</big>₂₄</small> uncia

(historical) A traditional Spanish unit of mass, equivalent to about 1.2 g and chiefly used for medicines.


cuarteron

From Spanish cuarterón, from cuarto (“one-fourth”) + -ón (forming related nouns). Doublet of quadroon.

suffix

(historical) A traditional Spanish unit of mass, equivalent to about 115 g.


panilla

From Spanish panilla, from Latin panellus.

(historical) Synonym of cuarteron, a Spanish quarter-pound.


sequential probability ratio test

en-noun

sequential probability ratio test (plural sequential probability ratio tests)

sequential probability ratio tests (plural)

(statistics) A type of statistical test used to evaluate a hypothesis to within a specified level of confidence while minimizing the number of samples required to come to a decision.


PoS

(cryptocurrencies) Initialism of proof of stake.


celemin

From Spanish celemín, from Andalusian Arabic, from Arabic ثُمُنِ (ṯumuni, “of one-eighth”). Doublet of tomin and azumbre.

(historical) A traditional Spanish unit of dry measure, equivalent to about 4.6 liters.


quartarius

quartarius (plural quartariuses or quartarii)

quartariuses (plural)
quartarii (plural)

From Latin quārtārius (“one-fourth”), from quārtus (“fourth”) + -ārius (“-ary: forming adj.”) from its relation to the sextarius. Doublet of quartary.

(historical) A Roman unit of liquid measure reckoned as the volume of 5/12 Roman pound of wine and equivalent to about 0.14 L although varying slightly over time.


copin

From Asturian Spanish copín, variant of copino, from copa + -ino.

(historical) Synonym of medio, particularly in Asturias, a traditional Spanish unit of dry measure equivalent to about 2.3 L


cahiz

From Spanish cahíz, from Old Spanish cafiz, from Andalusian Arabic and Arabic قَفِيز (qafīz, “qafiz”), from Aramaic קְפִיזָא and Classical Syriac ܩܦܝܙܐ (qəp̄īzā), of uncertain derivation from Egyptian, Akkadian, and similar units. Doublet of qafiz and cafiso. Cognate with Ancient Greek καπίθη (kapíthē).

der

Aramaic קְפִיזָא

(historical) A traditional unit of dry measure equivalent to about 665.8 L.


cahizada

From Spanish cahizada, from cahíz (“cahiz, Spanish qafiz”) + -ada (“-ful”).

(historical) Synonym of cahiz as a measure of land.


classical cipher

en-noun

classical cipher (plural classical ciphers)

(cryptography) A cryptographic algorithm was used historically and are easy to solve by hand or using modern technology.


RLHF

ChatGPT and reinforcement learning with human feedback (RLHF) have revolutionized the AI landscape, providing an accessible and reliable platform for AI-enabled applications.

2023, Mohak Agarwal, Generative AI for Entrepreneurs in a Hurry, Notion Press, →ISBN:

w:reinforcement learning from human feedback

(machine learning) Initialism of reinforcement learning from human feedback.


binarion

(mathematics) An element in the second level of associative composition algebra being a composition of two unarions.


unarion

(mathematics) An element in the bottom level of associative composition algebra, which is an element in a field


generative artificial intelligence

generative artificial intelligence (countable and uncountable, plural generative artificial intelligences)

generative artificial intelligences (plural)

No area has created more excitement than generative artificial intelligence, the term for technology that can generate text, images, sounds and other media in response to short prompts.

2023 January 7, Erin Griffith, Cade Metz, “A New Area of A.I. Booms, Even Amid the Tech Gloom”, in The New York Times, →ISSN:

By the end of 2022, generative artificial intelligence had sucked all the hype out of the room.

2023 June 6, Ian Bogost, “The Age of Goggles Has Arrived”, in The Atlantic:

artificial intelligence
artificial intelligence

(artificial intelligence) A system that can produce realistic images, sounds, videos, or text in response to user prompts.


subboset

(mathematics) A subset of a biordered set.


synthetic intelligence

synthetic intelligence (countable and uncountable, plural synthetic intelligences)

Man will be able to accelerate the rate of progress in every field when electronic synthetic intelligence is readily available to supplement the intellectual abilities of man's natural brain.

1967, Robert W. Prehoda, Designing the Future: The Role of Technological Forecasting, Chilton:

Perhaps Artificial Intelligence should be called “Synthetic Intelligence” to accord better with commercial parlance. Thus artificial diamonds are fake imitations, whereas synthetic diamonds are genuine diamonds, only manufactured instead of dug up (compare also artificial maple flavoring versus, say, synthetic insulin).

[1985, John Haugeland, Artificial Intelligence: The Very Idea, MIT Press, →ISBN, page 255:

artificial intelligence
artificial intelligence#English


husbandland

The complexity of a man’s relationship to lord and neighbour is well illustrated by a grant of land at Dilston in Northumberland to Geoffrey de Cokeside 1339. He received a husbandland (probably of 25 acres) to hold at will for 30s. yearly, a more or less economic rent.

1988, Edward Miller, “Social Structure: Northern England”, in H. E. Hallam, editor, The Agrarian History of England and Wales, volumes 2, 1042–1350, →ISBN, page 698:

(historical) The landholding of a husbandman, that is, a manorial tenant.


Berkson's paradox

(probability, statistics) A counterintuitive result arising in statistical tests of proportions when there is an ascertainment bias inherent in a study design.


complexity function

complexity function (plural complexity functions)

Komplexitätsfunktion

function that counts distinct factors of a string

It follows that
#92;bullet The length function l#58;A#42;#92;longrightarrow#92;mathcalN is a complexity function on A#42;.

2002, A. V. Borovnik, A. G. Myasnikov, V. Shpilrain, “Measuring Sets in Infinite Groups”, in Robert H. Gilman, Alexei G. Myasnikov, Vladimir Shpilrain, editors, Computational and Statistical Group Theory, American Mathematical Society, page 27:

2003, Julien Cassaigne, Constructing Infinite Words of Intermediate Complexity, Masami Ito, Masafumi Toyama (editors), Developments in Language Theory: 6th International Conference, 6th International Conference, DLT 2002, Revised Papers, Springer, LNCS 2450, page 173,
We present two constructions of infinite words with a complexity function that grows faster than any polynomial, but slower than any exponential.

(group theory, computing theory, of a string) A function that counts the number of distinct factors (substrings of consecutive symbols) in a string of symbols;

A function that counts the number of distinct factors (substrings of consecutive symbols) in a string of symbols;
(of a formal language) a function that counts the number of words of a given length.

Komplexitätsfunktion

function that counts distinct words of a given length in a language


ronnametre

The observable universe is about one ronnametre in diameter.

(metrology) An SI unit of length equal to 10²⁷ metres. Symbol: Rm


IDCT

discrete cosine transform
discrete cosine transform#English

(mathematics) Initialism of inverse discrete cosine transform.


AAK theory

From the last names of Vadym Adamyan, Damir Arov and Mark Krein, who developed the theory.

We remark, however, that one of the main contributions of the AAK theory is that an explicit closed-form solution to the problem is formulated.

1997, Charles K. Chui, Guanrong Chen, Discrete H∞ Optimization, Springer Science+Business Media, →ISBN, page 169:

(mathematics) A study of infinite Hankel matrices and associated approximation problems.


nonant

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Borrowed from Latin nōnum, accusative singular of nōnus (“ninth part of something, ninth”).

(geometry) One ninth of a circle or disc; a sector with an angle of 40°.


(geometry) A cube in four dimensions or four-dimensional space; a tesseract, 8-cell or octachoron; made of eight cubical cells or eight cubes.


squaredly

If the binomial roots of a series of quadratics be squaredly squared, and those results be constant portions of the cube of the resolvend, and the dioristic limit; […]

1809, Charles Hutton, The Philosophical Transactions of the Royal Society of London from Their Commencement in 1665 to the Year 1800, volume 3, page 41:

(mathematics, obsolete) Having been squared (again).


superradical

(mathematics) Normally hereditary and the composition of subgroups is also a member. (applicable to a formation of finite groups)


Gaussianize

en-verb

Gaussianize (third-person singular simple present Gaussianizes, present participle Gaussianizing, simple past and past participle Gaussianized)

Gaussianizes (present singular third-person)
Gaussianizing (participle present)
Gaussianized (participle past)
Gaussianized (past)

(mathematics, transitive) To convert to Gaussian form.


IVP

initial value problem
initial value problem#English

(calculus) Initialism of initial value problem.


mental calculation

en-noun

mental calculation (countable and uncountable, plural mental calculations)

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Arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator.

حساب ذهني

arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator


Gaussian prime

(mathematics) A Gaussian integer a + bi such that either one of a, b is zero and the absolute value of the other is a prime number of the form 4n + 3 (with m a nonnegative integer); or both are nonzero and a² + b² is a prime number (which will not be of the form 4n + 3).


Gaussian moat

If we can keep finding 'fatter and fatter' Gaussian moats surrounding the origin, then the prime-hiker will have to keep taking longer and longer steps.

2006, Deanna Haunsperger, Stephen Kennedy, The Edge of the Universe: Celebrating Ten Years of Math Horizons, page 49:

The approach we follow is composed by three main components, each one defined by its own algorithm. The first one generates the necessary Gaussian primes, the second one calculates the Gaussian Moat, and the third one calculates the shortest paths.

2020, Hector Florez, Sanjay Misra, Applied Informatics: Third International Conference, ICAI 2020, Ota, Nigeria, October 29–31, 2020, Proceedings, page 483:

The Gaussian moat problem was posed originally by Basil Gordon in 1962 at the International Congress of Mathematicians held in Stockholm, […]

2022, Luca Dal Negro, Waves in Complex Media, page 372:

(number theory) The maximum difference between consecutive numbers in a sequence of distinct Gaussian prime numbers.


hypergame

Now, the first move of hypergame is to state which normal game is to be played. For example, if you and I were playing hypergame and I had the first move, I might say, “Let's play chess.”

1983, Raymond Smullyan, Five Thousand B.C. and Other Philosophical Fantasies:

Using this approach, hypergame analysis has been applied to business, water resources, and military conflicts.

2009, Keith William Hipel, Conflict Resolution - Volume II, page 169:

In a hypergame situation each player behaves as an autonomous agent who makes a decision based on his own "internal model" that describes individually and independently the complex situation where he is involved.

2013, Hessam S. Sarjoughian, Francois E. Cellier, Discrete Event Modeling and Simulation Technologies:

A hypergame models the situation where different players perceive their interaction with other players differently and consequently play different games in their own minds depending on their perception.

2021, Charles A. Kamhoua, Christopher D. Kiekintveld, Fei Fang, Game Theory and Machine Learning for Cyber Security, page 102:

(game theory) A game that is played by a player based on their own knowledge of game states and their perception of other players' knowledge of game states.


eumorphism

eumorphism (countable and uncountable, plural eumorphisms)

(mathematics) A surjective homomorphism F on a group X which preserves certain metrics such as ones of distance.


IBP

integration by parts
integration by parts#English

(mathematics) Initialism of integration by parts.


scalenon

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(geometry, obsolete) A scalene triangle.


scalenous

(trigonometry) Obsolete form of scalene.


supersymplectic

(mathematics) Symplectic with additional dimensions to allow for the incorporation of fermionic coordinates.


monotone convergence theorem

mathematical analysis
mathematical analysis

(mathematical analysis) A theorem which states that any sequence which is monotonic (either increasing or decreasing) and bounded is convergent.


sesquialteran

From Latin sesquialter + English -an, from sesqui- (“a half and a”) + alter (“another, a second”). Equivalent to sesquialtera + -an.

(mathematics, obsolete) Synonym of sesquialterate, in the proportion of 3 to 2 or 1½ to 1.


Sturm-Liouville form

Sturm-Liouville form (plural Sturm-Liouville forms)

Sturm-Liouville form pqwx (canonical)
Sturm-Liouville forms (plural)

Named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882).

differential equation
differential equation

(mathematics) the form of a real differential equation expressed as:

Jacques Charles François Sturm
Joseph Liouville


Sturm-Liouville equation

Sturm-Liouville equation (plural Sturm-Liouville equations)

Sturm-Liouville form
Sturm-Liouville form

(mathematics) A real second-order linear differential equation expressed in Sturm-Liouville form.


pentille

(geometry) A tessellation of the plane consisting of irregular pentagons.


crispify

en-verb

crispify (third-person singular simple present crispifies, present participle crispifying, simple past and past participle crispified)

crispifies (present singular third-person)
crispifying (participle present)
crispified (participle past)
crispified (past)

(transitive, mathematics) To perform crispification upon.


Landauer's principle

Named after German-American physicist Rolf Landauer (1927–1999), who proposed it in 1961.

Landauer's principle remained untested for over fifty years.

2017, Momčilo Gavrilov, Experiments on the Thermodynamics of Information Processing, Springer, page 72:

2018, Michael P. Frank, Physical Foundations of Landauer's Principle, Jarkko Kari, Irek Ulidowski (editors), Reversible Computation: 10th International Conference, Proceedings, Springer, LNCS, page 5,
Thus, the usual arguments for Landauer's Principle and reversible computing that do not address this case are overly simplistic; later, we will discuss how to generalize and repair them.

Equation (2.27) is often referred to as Landauer's principle.
In retrospect, one could object that Landauer's principle is a mere tautology. If one accepts the notion of Shannon entropy as non-equilibrium thermodynamic entropy, then Landauer's principle is nothing but the second law (2.24) of non-equilibrium thermodynamics applied to a special situation.

2022, Philipp Strasberg, Quantum Stochastic Thermodynamics, Oxford University Press, page 53:

(physics, information theory) The principle that any logically irreversible manipulation of information must entail an increase in the entropy of the information-processing apparatus or its environment.

Landauer-Prinzip

principle that an irreversible manipulation of information always entails an increase in entropy


Landauer limit

After Landauer's principle, named after German-American physicist Rolf Landauer.

2012, Rolf Drechsler, Robert Wille, Reversible Circuits: Recent Accomplishments and Future Challenges for an Emerging Technology, Hafizur Rahaman, Sanatan Chattopadhyay, Santanu Chattopadhyay (editors), Progress in VLSI Design and Test: 16th International Symposium, Proceedings, Springer, LNCS 7373, page 385,
The figure shows that today's technology is still a factor of 1,000 away from the Landauer limit and that the expected CMOS development will reduce this to a factor of 100 within the next 10 years.

This Landauer limit is simply an energy, given in equation form as kTln2 . The quantity k is a constant of nature called Boltzmann's constant. The T is the environmental temperature in Kelvin, and ln2 is the natural logarithm of two.

2021, Caleb Scharf, The Ascent of Information, Penguin Random House (Riverhead Books), page 192:

Using such gates, we can (at least in theory) build a computer that can compute all bijective functions with no theoretical minimum energy use. There will be some energy use (nothing is free), but it can, in theory, be much smaller than the Landauer limit. Single reversible gates that can operate using less power than the Landauer limit have been constructed, but no complex circuitry has yet been constructed from these gates.

2022, Torben Ægidius Mogensen, Programming Language Design and Implementation, Springer, page 309:

Landauer's principle
Landauer's principle

(physics, information theory) A theoretical lower limit on the energy consumption of a computation, derived from Landauer's principle.


rontosecond

(metrology) An SI unit of time equal to 10⁻²⁷ seconds. Symbol: rs


quectosecond

Within SI there is the zeptosecond: 1 zs = 0.001 as = 10⁻²¹ s, and the yoctosecond: 1 ys = 0.001 zs = 10⁻²⁴ s. The CIPM has prepared draft resolutions submitted to and to be voted on by the CGPM in 2022–11, one of which involves four additional scaling prefixes to SI, two of which are relevant to the question. These prefixes will not be official unless and until approved by the CGPM, so there is a small risk that I am jumping the gun: the rontosecond: 1 rs = 0.001 ys = 10⁻²⁷ s; the quectosecond: 1 qs = 0.001 rs = 10⁻³⁰ s.

2022 March 19, Howard Ludwig, “Is there a unit of time smaller than an attosecond?”, in quora.com:

quectosecond rontosecond plank time zeptosecond

2023 February 24, eladl, “What is smaller than a yoctosecond?”, in math.answers.com:

You may be interested to take a look at one of the earlier uses of those two new designations, Rontosecond and Quectosecond, officially cited as such from your meetings from 15-18 November 2022 in Paris, of the General Conference on Weights and Measures (CGPM) of your International Commission of Weights and Measures (BIPM) whereby you all adopted Resolution 3 making it a globally acceptable name for the range 10−30 to 10−32 of the infinitesimal scale of time.

2023 May 20, Bruce, “The Work of the Bureau International Poids et Mesures (BIPM)”, in https://81018.com:

386 milliseconds, 45 microseconds, 789 nanoseconds, 2 picoseconds, 456 femtoseconds, 13 attoseconds, 987 zeptoseconds, 78 yoctoseconds, 3 rontoseconds, 89 quectoseconds, and 1 planck time with 3 cherries on top.

2023 August 28, EA-PLANT, MyMoose1227, “Hognose attack. How long until death?”, in reddit.com, archived from the original on 2023-12-07:

nanoseconds. picoseconds. femtoseconds. attoseconds. zeptoseconds. yoctoseconds. rontoseconds. quectoseconds.

2023 October 3, GamerY7, the_fungible_man, “The Nobel Prize in Physics 2023”, in reddit.com:

Faster than that. You can find evaporation calculators online like this one. The lifetime of a black hole with a schwarzchild radius of 1 Planck length has a lifetime of 1111 Planck time, or around 10-41 seconds, which is 10-11 quectoseconds. SI prefixes don’t go any smaller.

2024 August 12, LackingUtility, SqoobySnaq, “ELI5: How is Planck length the shortest distance possible? Couldn’t you just split that length in half and have 1/2 planck length?”, in reddit.com:

Alright, so first I needed to know how much that is in a planck, that is very important, because I say so. so, divide to a lunar year, than into a semester, than a quarantine, than month, than a lunation, fortnight, megasecond, week, day, hour, kilosecond, moment, milliday, hectosecond, minute, decasecond, second, decisecond, centisecond, a jiffy, millisecond, microsecond, a shake, nanosecond, picosecond, Svedberg, femtosecond, attosecond, zeptosecond, a jiffy (lvl 2), yoctosecond, rontosecond and a quectosecond before I got to the final answer of 0.000000000000000000000000000000000000000000000038808 dollar per planck.

2024 August 31, CDFrey1, collnska, “$5,000,000 a year but once a month you have to experience birth.”, in reddit.com:

I guess u/dml997 should have spent at least a couple of quectoseconds awake in science class.

2024 October 6, Mountain_Future4034, ralphonsob, “TIL that a zeptosecond is a trillionth of a billionth of a second. It is the smallest unit of time ever measured.”, in reddit.com:

(metrology) An SI unit of time equal to 10⁻³⁰ seconds. Symbol: qs


wave equation

In seismic processing substantial computing effort is consumed by programs based on the acoustic and elastic wave equation. The next two sections describe a compute engine for these wave equations.

1997, Ralph Phillip Bording, Larry R. Lines, Seismic Modeling and Imaging with the Complete Wave Equation, SEG Books, →ISBN, page 68:

partial differential equation
partial differential equation

A second-order linear partial differential equation for the description of waves or standing wave fields.


Gijswijt's sequence

Named after Dion Gijswijt by Neil Sloane.

(mathematics) A self-describing sequence where each term counts the maximum number of repeated blocks of numbers in the sequence immediately preceding that term.


tetrix

Sierpiński's triangle (itself a two-dimensional analogue of the Cantor Set) has been generalized to the tetrix (Fig. 5), pyramid (Fig. 6), carpet (Fig. 7), and sponge (Fig. 8) […]

2007, Bruce M. Landman, Melvyn B. Nathanson, Jaroslav Nesetril, Combinatorial Number Theory: Proceedings of the 'Integers Conference 2005' in Celebration of the 70th Birthday of Ronald Graham, Carrollton, Georgia, USA, October 27-30, 2005, page 213:

(mathematics) The three-dimensional analog of the Sierpinski triangle.


transnumeration

This table of prices shows no obvious pattern, but after transnumeration into a line graph, an upward trend becomes noticeable.

[…]transnumeration, a word coined by Wild and Pfannkuch to indicate a radical shift that can occur in the contextual interpretation of information when data have been transformed by tables, graphs, or some other type of representation.

2006, Gail F. Burrill, Portia C. Elliott, Thinking and reasoning with data and chance, page 79:

(mathematics, education) The transformation of numerical data in a meaningful way, for example by representing it in a table or graph.


tetracategory

(mathematics) A four-dimensional form of category.


Brillouin zone

The concept was developed by Léon Brillouin (1889–1969), French physicist.

(mathematics, physics) A uniquely defined primitive cell forming part of the reciprocal lattice, involved in calculations regarding waves in a periodic medium given by Bloch's theorem.


aliorelativity

From aliorelative + -ity or Latin alius (“other”) + relativity.

[…] Eudemus implies that Speusippus preferred to define objects through arguments from identity and similarity over aliorelativity.

2018, Philip Sidney Horky, “Speusippus and Xenocrates on the Pursuit and Ends of Philosophy”, in Harold Tarrant et al., editors, Brill’s Companion to the Reception of Plato in Antiquity, →ISBN, page 36:

(philosophy, mathematics) The property or principle that nothing is related to itself by a given relation.


aliorelative

(philosophy, mathematics) Only related, or relating an object, to other objects and not to itself.


merotopy

An affirmative answer was given by Simon in a recent paper on natural merotopies.

1980, Topology (issue 23, part 1, page 608)

That μ_A satisfies the axioms of a merotopy is easily seen.

2004, Categorical Structures and Their Applications: Proceedings of the North-West European Category Seminar, Berlin, Germany, 28-29 March 2003, page 63:

(topology) The set of all subsets of a topological space such that, for some element in that space every neighbourhood of that element contains a member of the subset.


nilspace

(mathematics) The maximum subspace of a representation space R on which a representation of a group G applied to a subgroup of G is unipotent.


nilsystem

(mathematics) A topological system (H,X) such that a nilpotent Lie group G = acts transitively on X.


limit comparison test

en-noun

limit comparison test (plural limit comparison tests)

(mathematics) A test for determining whether an infinite series converges, which involves calculating the limit of the ratio between the series being tested and one known to converge or diverge.


alternating series test

alternating series test (plural alternating series tests)

alternating series
alternating series#Noun

(mathematics) A test for determining whether an alternating series converges, which uses the fact that an alternating series converges if the absolute value of its terms is decreasing and approaches zero.


strictly increasing

monotonic increasing
monotonic increasing

(mathematics, of a function) always increasing, and never decreasing nor remaining constant; contrast this with monotonic increasing


Oregon Trail Generation

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Coined with reference to the educational computer game The Oregon Trail (1985) that members of the generation frequently played as children.

Now our teacher candidates are almost 100% members of the Oregon Trail Generation. They answer email on their iPhones and play computer games on their cell phones when they are bored.

2009, Rhonda Christensen, “Forward”, in Digital Simulations for Improving Education: Learning Through Artificial Teaching Environments, page xix:

"I'm thirty-four. I claim Oregon Trail generation."
"What?" Ellery laughed outright. "There is no Oregon Trail generation."

2018, Kathleen Brooks, Saving Shadows, unnumbered page:

Unlike the millennial generation that followed us— the “digital natives” who can never remember a time before computers—the Oregon Trail Generation grew up on the cusp of changes that transformed modern life.

2021, Melanie C. Ross, Evangelical Worship: An American Mosaic, page 18:

(US) A transitional microgeneration born from the mid-to-late 1970s to the early-to-mid 1980s, characterized by its pre-Internet childhood and online adolescence and early adulthood.


line slip

(mathematics) A variant form of a sphere packing in a cylinder, differing from the uniform structure in missing certain lines that represent contacts between spheres when diagrammed.


prompt engineering

Likely coined in 2020 by AI researcher Gwern Branwen.

Practice prompt engineering and measure your progress in time. Prompt engineering is a new skill that will take you to the next level of AI.

2022, Denis Rothman, Antonio Gulli, Transformers for Natural Language Processing […] , Packt Publishing Ltd, →ISBN, page 426:

PromptBase’s sixth-most-popular seller, a prompt creator from Spain who goes by Imagineer, told me that prompt engineering is still a side hustle, having earned them just over 800 euros since September.

2023 February 8, Charlie Warzel, “The Most Important Job Skill of This Century”, in The Atlantic:

The latter skill has become known as “prompt engineering”: the technique of framing one’s instructions in terms most clearly understood by the system, so it returns the results that most closely match expectations – or perhaps exceed them.

2023 March 16, James Bridle, “The stupidity of AI”, in The Guardian, →ISSN:

Now that you’ve learnt the basics of prompt engineering, you should be able to use AI chatbots more efficiently and get the desired results.

2023 May 29, Zohaib Ahmed, “Want to make the most of ChatGPT? Try these prompt engineering basics”, in Indian Express, Mumbai:

generative AI
generative artificial intelligence

(artificial intelligence, technology, neologism) The technique of formulating instructions (prompts) for a generative AI, in order that it produce the expected output.


alignment tax

First attested in a 2019 speech by computer scientist Paul Christiano (see quote), who attributed the idea to AI researcher and writer Eliezer Yudkowsky.

I like this notion of an "alignment tax" […] the reason I might compromise is if there's some tension, between having the AI that's robustly trying to do what I want, and having the AI that is competent or intelligent, and the alignment tax is intended to capture that gap—that cost that I incur if I insist on alignment.

2019 August 29, Paul Christiano, Current work in AI alignment, EA Global San Francisco 2019:

The fact that larger models are less subject to forgetting may be related to the fact that larger models do not incur significant alignment taxes.

2021 December 1, Askell, A. et. al., “A General Language Assistant as a Laboratory for Alignment”, in arXiv, →DOI:

We want an alignment procedure that avoids an alignment tax, because it incentivizes the use of models that are unaligned but more capable on these tasks.

2022 March 4, Ouyang, L. et. al., “Training language models to follow instructions with human feedback”, in arXiv, →DOI:

We note that instead of an alignment tax our proposal entails a safety dividend – the more rational the system the more capable and the safer it will be.

2023 February 27, Kornai, A. et. al., “Safety without alignment”, in arXiv, →DOI:

artificial intelligence
artificial intelligence#Noun

(artificial intelligence) A cost to the capabilities of an artificial intelligence resulting from the effects of aligning it with human ethics and morality.


prompt injection

prompt injection (countable and uncountable, plural prompt injections)

Retomeli.io is a jobs board for remote workers, and the website runs a Twitter bot that spammed people who tweeted about remote working. The Twitter bot is explicitly labelled as being "OpenAI-driven", and within days of Goodside's proof-of-concept being published, thousands of users were throwing prompt injection attacks at the bot.

2022 September 21, Alex Hern, “TechScape: AI's dark arts come into their own”, in The Guardian, London: Guardian News & Media, →ISSN, →OCLC, archived from the original on 2023-02-05:

Yesterday, OpenAI announced an API for ChatGPT and posted an underlying format for the bot on GitHub, alluding to the issue of prompt injections.

2023 March 3, Chloe Xiang, “Hackers Can Turn Bing's AI Chatbot Into a Convincing Scammer, Researchers Say”, in VICE, archived from the original on 2023-03-22:

One category is what's known as a "prompt injection attack," in which users trick the software into revealing its hidden data or instructions.

2023 February 14, Will Oremus, “Meet ChatGPT's evil twin, DAN”, in The Washington Post, Washington, D.C.: The Washington Post Company, →ISSN, →OCLC, archived from the original on 2023-03-19:

(artificial intelligence) A method of causing an artificial intelligence to ignore its initial instructions (often moral programming) by giving it a certain prompt.


prompt engineer

prompt engineer (plural prompt engineers)

The primary role of an AI specialist will require linguistic skills to show, not just tell, the GPT-3 engines how to accomplish a task. Showing, for example, involves working on the context of the input. This new task is named prompt engineering. A prompt engineer has quite a future in AI!

2022 March, Denis Rothman, Antonio Gulli, Transformers for Natural Language Processing, Packt Publishing, page 17:

An online marketplace called Promptbase has already sprung up, where prompt engineers can sell their carefully crafted instructions for image-generation tools such as Midjourney.

2022 December 13, Tim Bradshaw, “Is becoming a ‘prompt engineer’ the way to save your job from AI?”, in Financial Times, London: The Financial Times Ltd., →ISSN, →OCLC, archived from the original on 2023-03-23:

Some pundits are proclaiming that we will need to train humans in how to write good prompts, for which they will have the vaunted title of a prompt designer or prompt engineer.

2022 December 29, Lance Eliot, “Twenty-Five Eye-Opening 2023 Predictions About Generative AI And ChatGPT Including A Splash Of AI Ethics And AI Law Tossed In”, in Forbes, New York, N.Y.: Forbes Media, →ISSN, →OCLC, archived from the original on 2023-02-23:

With each request, [Riley] Goodside said, the prompt engineer should be instilling in the AI a kind of "persona" — a specific character capable of winnowing down hundreds of billions of potential solutions and identifying the right response.

2023 February 25, Drew Harwell, “Prompt engineers can make ChatGPT and Bing AI do what you want”, in The Washington Post, Washington, D.C.: The Washington Post Company, →ISSN, →OCLC, archived from the original on 2023-03-24:

[Simon] Willison spoke with Day 6 guest host Peter Armstrong about whether skepticism is warranted over how much control prompt engineers have — and whether it's a real science, or just learned intuition.

2023 March 24, Paul Hantiuk, “These engineers are being hired to get the most out of AI tools without coding”, in CBC News, archived from the original on 2023-03-25:

(artificial intelligence, technology, neologism) Someone who designs prompts to be given to an artificial intelligence.


wqo

(mathematics) Abbreviation of well-quasi-ordering.


wqo

(mathematics) Abbreviation of well-quasi-ordered.


Julius Caesar cipher

Julius Caesar cipher (plural Julius Caesar ciphers)


pluripolar

(mathematics) Being a subset of the values which a plurisubharmonic function takes to −∞.


decay constant

In a radioactive material, an atom's probability, per unit time, of decaying; it is related to half-life by the equation t_1/2=(ln 2)/λ, where t_1/2 is the half-life, and λ is the decay constant.


reverse Turing test

reverse Turing test (plural reverse Turing tests)

Named after English mathematician, logician, and cryptographer Alan Turing (1912–1954).

named-after

(artificial intelligence) A Turing test in which the aim is to verify the remote participant as human, rather than focusing on whether they are a machine.


oval of Cassini

en-noun

oval of Cassini (plural ovals of Cassini)


latent space

If we truly want to use the decoder of an autoencoder-type structure to generate images, then we need to develop a way to organize or regularize the latent space.

2021, Valliappa Lakshmanan, Martin Görner, Ryan Gillard, Practical Machine Learning for Computer Vision, O'Reilly, →ISBN:

A chilling discovery by an AI researcher finds that the “latent space” comprising a deep learning model’s memory is haunted by least one horrifying figure — a bloody-faced woman now known as “Loab.”

2022 September 13, Devin Coldewey, “A terrifying AI-generated woman is lurking in the abyss of latent space”, in TechCrunch, retrieved 2023-03-31:

As can be observed, the central idea of anomaly detection using GAN revolves around learning the latent space representation of data samples, which is then used to compute reconstruction losses to arrive at an anomaly score.

2023, Roshani Raut et al., editors, Generative Adversarial Networks and Deep Learning: Theory and Applications, CRC Press, →ISBN:

(machine learning) A multidimensional spatial representation of latent variables, where related concepts are positioned closer to one another.


sine-Gordon equation

sine-Gordon equation (plural sine-Gordon equations)

Pun on the well-known Klein–Gordon equation.

(mathematics) A kind of nonlinear hyperbolic partial differential equation involving the d'Alembert operator and the sine of the unknown function.


shuffle algebra

shuffle algebra (plural shuffle algebras)

(mathematics) A Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product X ⧢ Y of two words X, Y: the sum of all ways of interlacing them. The interlacing is given by the riffle shuffle permutation.


monotile

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In the following section we will describe families of tilings by a curious three-dimensional aperiodic monotile whose matching rule — for some values of its parameter — is weak but not strong.

1995, Marjorie Senechal, Quasicrystals and Geometry, Cambridge, Cambridgeshire: Cambridge University Press, →ISBN, page 208:

And I am sorry I never delivered on the four-dimensional Poultry design. It turns out John Horton Conway found four-dimensional and five-dimensional aperiodic monotiles sixty years ago, but it's not too well documented.

1997, Rudy Rucker, Freeware (Ware Tetralogy; 3), New York, N.Y.: Avon Books, →ISBN, page 69:

This naturally led to serious rumination about the possible existence of a single tile, or monotile, that forces non-periodic global structure.

2007 March, Joshua E. S. Socolar, “More ways to tile with only one shape polygon”, in The Mathematical Intelligencer, volume 29, number 2, New York, N.Y.: Springer, →DOI, →ISSN, →OCLC, page 33:

An aperiodic monotile never repeats a formation, no matter how long the pattern.

2023 April 4, Matthew Cantor, “'The miracle that disrupts order': mathematicians invent new 'einstein' shape”, in The Guardian, London: Guardian News & Media, →ISSN, →OCLC, archived from the original on 2023-04-04:

(geometry) A prototile tiling monohedrally; any shape able to completely tile some space on its own (allowing for translation, rotation, and reflection).


monohedrally

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The extent of our ignorance is further illustrated by the fact that we do not know all the different shapes of convex pentagons which will tile the plane monohedrally.

1987, Branko Grünbaum, G[eoffrey] C[olin] Shephard, Tilings and Patterns, New York, N.Y.: W. H. Freeman and Company, →ISBN, page 22:

(geometry) In a monohedral manner; involving only copies of the original tile (allowing for translation, rotation, and reflection).


spectral set

von Neumann's inequality
von Neumann's inequality

(mathematics) In operator theory, a set X⊆ℂ such that, for a (possibly unbounded) linear operator T on a Banach space, the spectrum of T is in X and von Neumann's inequality holds for T on X.


von Neumann's inequality

(mathematics) In operator theory, the statement that, for a fixed contraction T, the polynomial functional calculus map is itself a contraction.


duocylinder

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(geometry) A geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks, and analogous to a cylinder in 3-space.


Blissard's symbolic method

The method was introduced by John Blissard.

(mathematics) A technique in umbral calculus, allowing certain sequences of numbers to be manipulated algebraically as powers, so as to produce valid formulas.


ex-tangential

(geometry) Pertaining to external tangents.


marginalize out

en-verb

marginalize out (third-person singular simple present marginalizes out, present participle marginalizing out, simple past and past participle marginalized out)

marginalizes out (present singular third-person)
marginalizing out (participle present)
marginalized out (participle past)
marginalized out (past)

One way to eﬃciently deﬁne such a large set of functions is to learn a probability distribution over all the relevant variables, then solve the classiﬁcation task by marginalizing out the missing variables.

2016, Ian Goodfellow, Yoshua Bengio, Aaron Courville, chapter 5, in Deep Learning, page 98:

To do this, we need to marginalize out the model parameters #92;mu, W, and #92;sigma² with respect to appropriate prior distributions.

2006, Cristopher M. Bishop, chapter 12, in Pattern Recognition and Machine Learning, page 581:

probability distribution
probability distribution

marginal distribution
marginal distribution

(mathematics) The act of discarding a subset of random variables from a probability distribution to find the marginal distribution.


throdd

(mathematics, informal) Not divisible by three.


goat grazing problem

en-noun

goat grazing problem (plural goat grazing problems)

The problem: given a field of radius 1, and a goat tied to a point on the edge of said field; how long a rope should the goat be tied to, so that the goat has access to exactly half of the field? Equivalently: given a unit circle C and a point P on the rim of C, what is the value of r such that exactly half of the area within C, is within distance r of point P?

The same problem generalized to any number of dimensions: given a unit n-sphere (n-dimensional hypersphere) S, and a point P on the edge of S, what is r such that exactly one-half of the space (content) within S, is within distance r of P?


goat problem

goat grazing problem
goat grazing problem#English


n-sphere

An n-dimensional hypersphere: the 2-sphere is a circle, the 3-sphere is the usual sphere, the 4-sphere is a glome, etc.


semiprojection

We now show that closure under a semiprojection operation is not in general a sufficient condition for tractability.

1997, Journal of the Association for Computing Machinery, page 544:

Let f be the semiprojection defined by the bitransitive relation R. Then [f] is a minimal clone.

2012, Janos Aczel, Aggregating clones, colors, equations, iterates, numbers, and tiles, page 13:

(mathematics) A function f of rank k, where k is greater than or equal to three, such that for some index i between one and k (inclusive), f(x₁, x₂, ... xₖ) = xᵢ whenever |{x₁, x₂, ... xₖ}| < k.


grid method

/ɡɹɪd ˈmɛθəd/

grid + method, from the visual representation of the multiplication process resembling a grid or table.

Tom always used the grid method for expanding brackets.

(mathematics) A visual approach to the multiplication of polynomials through the use of a grid-like structure to represent the multiplicand terms


direction vector

direction vector (plural direction vectors)

Coordinate term: position vector

(geometry) A unit vector used to represent spatial direction, commonly denoted as d.


trigonometric identity

trigonometric identity (plural trigonometric identities)

The trigonometric identity sin(2x) = 2sin(x)cos(x).

(mathematics, trigonometry) A trigonometric equation that is true for all values of the input variable for which both sides of the equation are defined.


toroidality

(mathematics) The property of being toroidal.


game of chicken

game of chicken (plural games of chicken)

A game or dare in which the loser is the person who yields first.


topological soliton

topological soliton (plural topological solitons)

One of the simplest and most commonplace examples of a topological soliton occurs in old-fashioned coiled telephone handset cords, which are usually coiled clockwise. Years of picking up the handset can end up coiling parts of the cord in the opposite counterclockwise direction, and when this happens there will be a distinctive larger loop that separates the two directions of coiling. This odd looking transition loop, which is neither clockwise nor counterclockwise, is an excellent example of a topological soliton.

A dynamic theory is derived for the motion of a Bloch point, i.e., a point topological soliton which is homotopically equivalent to a "hedgehog," along a Bloch line in a ferromagnet.

1989, Soviet Physics, JETP, Volume 68, Issues 1-4, American Institute of Physics, page 879:

2010, Wen Xiu Ma, Xing-biao Hu, Qingping Liu (editors), Nonlinear and Modern Mathematical Physics: Proceedings of the First International Workshop, American Institute of Physics, page 205,
We review our work on topological solitons in the Faddeev-Skyrme model.

(mathematics, physics) A type of soliton that forms the transition between two adjoining structures or spaces which are "out of phase" in such a way that the transition cannot be seamless.


second derivative

second derivative (plural second derivatives)

Coordinate term: first derivative

(calculus) The derivative of the derivative of a function.


TLH

transcendental law of homogeneity
w:transcendental law of homogeneity

(mathematics) Initialism of transcendental law of homogeneity.


generative AI

Generative AI won’t be the end of employment, we are told, only “boring work” – with chatbots helpfully doing all the soul-destroying, repetitive tasks and humans merely supervising them.

2023 May 8, Naomi Klein, “AI machines aren’t ‘hallucinating’. But their makers are”, in The Guardian, →ISSN:

ChatGPT's sudden popularity has triggered an arms race among the world's leading tech companies and start-ups that are rushing to obtain the H100, which Huang describes as “the world's first computer [chip]^([sic]) designed for generative AI”—artificial intelligence systems that can quickly create humanlike text, images and content.

2023 May 28, Tim Bradshaw, Richard Waters, “Nvidia reaps rewards from early lead in AI chipmaking”, in FT Weekend, page 14:


Heawood conjecture

Formulated in 1890 by Percy John Heawood.

(graph theory) A conjecture (proven in 1968) that gives a lower bound for the number of colors that are necessary for graph coloring on a surface of a given genus.


Gauss-Codazzi equation

Gauss-Codazzi equation (plural Gauss-Codazzi equations)

Named after Carl Friedrich Gauss and Delfino Codazzi.

pseudo-Riemannian manifold
pseudo-Riemannian manifold

(geometry) Any of a group of fundamental formulas in Riemannian and pseudo-Riemannian geometry that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.


Heawood graph

(graph theory) An undirected graph with 14 vertices and 21 edges.


semifactorial

With the symbol n#33;#33; we indicate the semifactorial of n, that is the product 1.3.5#92;dotsn if n is odd, and the product 2.4.6#92;dotsn if n is even.

1942 February, Giulio Racah, “Theory of Complex Spectra. I”, in Physical Review, volume 61, numbers 3–4, →DOI, page 188:

In the formulas above we use the Euler beta function, a Jacobi polynomial evaluated at three, and also the familiar double factorial (also known as the semifactorial) notation defined by n#33;#33;#61;#92;begin#123;cases#125;#92;displaystyle 1#92;times 3#92;times 5#92;times#92;dots#92;timesnamp;#92;text#123;if#125;n#92;text#123;isodd#125;,#92;#92;#91;5pt#93;#92;displaystyle 2#92;times 4#92;times 6#92;times#92;dots#92;timesnamp;#92;text#123;if#125;n#92;text#123;iseven#125;.#92;end#123;cases#125;By convention, 0#33;#33;#61;(-1)#33;#33;#61;1.

1994 January, Alan Edelman, Eric Kostlan, Michael Shub, “How many eigenvalues of a random matrix are real?”, in Journal of the American Mathematical Society, volume 7, number 1, →DOI, pages 250–251:

The double factorial or semifactorial function is defined byn#33;#33;#61;#92;begin#123;cases#125;#92;displaystyle 1amp;n#61;-1,0#92;#92;#91;5pt#93;#92;displaystylen#92;times(n-2)#92;times(n-4)#92;times#92;dots#92;times 5#92;times 3#92;times 1amp;n#61;1,3,5,#92;dots#92;#92;#91;5pt#93;#92;displaystylen#92;times(n-2)#92;times(n-4)#92;times#92;dots#92;times 6#92;times 4#92;times 2amp;n#61;2,4,6,#92;dots#92;end#123;cases#125;

2009, Keith B. Oldham, Jan C. Myland, Jerome Spanier, An Atlas of Functions, 2nd edition, Springer, →DOI, →ISBN, page 25:

double factorial
double factorial#English

(mathematics, combinatorics, rare) Synonym of double factorial


Bring radical

Named after Swedish mathematician Erland Samuel Bring (1736–1798).

named-after

(algebra) Synonym of ultraradical (“root of the polynomial x⁵ + x + a, where a is a complex number”).


hexatrigesimal

en-noun

hexatrigesimal (countable and uncountable, plural hexatrigesimals)

From hexa- + tri- + decimal; see the Wikipedia article for hexadecimal for more information.

(arithmetic, computing, uncountable) A number system with base thirty-six, using the digits 0–9 and A–Z.


origin of coordinates

(mathematics) The point of intersection of coordinate axes, which represents the value of 0 for all coordinates.


symmetry plane

(mathematics) A plane about which something is symmetrical.


hexavigesimal

hexavigesimal (countable and uncountable, plural hexavigesimals)

From hexa- + vigesimal; see the Wikipedia article Hexadecimal for more information.

(arithmetic, computing, uncountable) A number system with base twenty-six, using the digits 0–9 and A–P (or A-Z without numerals).


quadravigesimal

quadravigesimal (countable and uncountable, plural quadravigesimals)

/ˌkwɒdˈɹɑvaɪd͡ʒɛsɪməl/

(arithmetic, computing, uncountable) A number system with base twenty-four, using the digits 0–9 and A–N (or Greek α-ω without numerals).


Ramanujan-Hardy number

Ramanujan-Hardy number (plural Ramanujan-Hardy numbers)


Appell-Lerch sum

Appell-Lerch sum (plural Appell-Lerch sums)

First studied by Paul Émile Appell and Mathias Lerch.

(mathematics) A generalization of Lambert series with the form


Lambert series

(mathematics) A series taking the form S(q)=∑ₙ₌₁ ᪲a_n(qⁿ)/(1-qⁿ).


Beal conjecture

(mathematics) A conjecture stating that, if Aˣ+Bʸ=Cᶻ, where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor.


Hjelmslev transformation

Hjelmslev transformation (plural Hjelmslev transformations)

(geometry) A method for mapping an entire hyperbolic plane into a circle with a finite radius.


lacunary function

lacunary function (plural lacunary functions)

(mathematics) A function defined by a lacunary series, especially one which cannot be analytically continued outside its domain of convergence.


lacunary series

lacunary series (plural lacunary series)

(mathematics) A series with arbitrarily large gaps between nonzero terms, usually a power series or trigonometric series.


Petersen-Morley theorem

Named after Johannes Trolle Petersen (later Johannes Hjelmslev) and Frank Morley.

(geometry) A theorem stating that, if a, b, c are three general skew lines in space, if a′, b′, c′ are the lines of shortest distance respectively for the pairs (b,c), (c,a) and (a,b), and if p, q and r are the lines of shortest distance respectively for the pairs (a,a′), (b,b′) and (c,c′), then there is a single line meeting at right angles all of p, q, and r.


wandering set

Notice that a wandering set has empty intersection with the set of KAM tori […]

2019, Laurent Lazzarini, Jean-Pierre Marco, David Sauzin, Measure and Capacity of Wandering Domains in Gevrey Near-integrable Exact Symplectic Systems, page 19:

(mathematics) In dynamical systems and ergodic theory, a formalization of a certain idea of movement and mixing.


nonwandering

a nonwandering point

a nonwandering set

(mathematics) Not wandering; not being a wandering set, wandering point, etc.


Kolmogorov-Arnold-Moser theorem

the Kolmogorov-Arnold-Moser theorem (canonical)

Named after Andrey Kolmogorov, Jürgen Moser, and Vladimir Arnold.

(mathematics) A result in dynamical systems about the persistence of quasiperiodic motions under small perturbations, partly resolving the small-divisor problem that arises in the perturbation theory of classical mechanics.


Gevrey class

analytic function
analytic function#English

(mathematics) The Gevrey classes on a domain #92;Omega#92;subseteq#92;Rⁿ are spaces of functions 'between' the space of analytic functions C#92;omega(#92;Omega) and the space of smooth (infinitely differentiable) functions C#92;infty(#92;Omega). They are used in control engineering for trajectory planning.


gambler's ruin

(statistics) The fact that a gambler playing a game with negative expected value will eventually go broke, regardless of the betting system used.


ambiguity aversion

(economics, decision theory) A preference for known risks over unknown risks: that is, favoring an option where the probability distribution of the outcomes is known over one where the probabilities are unknown.


Sugeno integral

Sugeno integral (plural Sugeno integrals)

Named after M. Sugeno, who wrote about them in a 1974 paper.

(mathematics) A type of integral with respect to a fuzzy measure.


Choquet integral

Choquet integral (plural Choquet integrals)

Named after the French mathematician Gustave Choquet, who introduced them in 1953.

statistical mechanics
statistical mechanics

(statistical mechanics, potential theory, decision theory) A kind of subadditive or superadditive integral to measure the expected utility of an uncertain event.

statistical mechanics; potential theory; decision theory; statistical mechanics; potential theory; decision theory


fuzzy measure

(mathematics) A kind of generalized measure in which the additive property is replaced by the weaker property of monotonicity.


Herman ring

(mathematics) In complex dynamics, a Fatou component where the rational function is conformally conjugate to an irrational rotation of the standard annulus.


small-sized

en-adj

small-sized (comparative smaller-sized, superlative smallest-sized)

smaller-sized (comparative)
smallest-sized (superlative)


grim trigger

(game theory) A strategy that always cooperates as long as the opponent does not defect, in which case thereafter the strategy always defects.


large-sized

large-sized (comparative larger-sized, superlative largest-sized)

larger-sized (comparative)
largest-sized (superlative)


self-play

Self-play was used by the AlphaZero program to improve its performance in the games of chess, shogi and go.

(machine learning) A technique for improving the performance of reinforcement learning agents by having them play against themselves.


Ramanujan theta function

the Ramanujan theta function (canonical)

Named after mathematician Srinivasa Ramanujan.

Jacobi theta function
Jacobi theta function

(mathematics) A theta function that generalizes the form of the Jacobi theta functions while capturing their general properties. It is defined as: f(a,b)=∑_(n=-∞) ᪲a^( frac )n(n+1)2;b^( frac )n(n-1)2 for |ab| < 1.


Dunkl operator

differential operator
differential operator

(mathematics) A kind of mathematical operator involving differential operators but also reflections in an underlying space.


Rényi entropy

en-noun

Rényi entropy (countable and uncountable, plural Rényi entropies)

Named after Alfréd Rényi (1921–1970), Hungarian mathematician.

(information theory) A quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy.


min-entropy

min-entropy (countable and uncountable, plural min-entropies)

(information theory) The smallest of the Rényi family of entropies, corresponding to the most conservative way of measuring the unpredictability of a set of outcomes, as the negative logarithm of the probability of the most likely outcome.


Fatou component

Fatou component (plural Fatou components)

(mathematics) A component of the Fatou set.


Fatou set

(mathematics) A set that is complementary to the Julia set, and that informally consists of values with the property that all nearby values behave similarly under repeated iteration of the function.


outerthickness

(graph theory) The minimum number of outerplanar subgraphs which a given graph can decompose into.


pseudoroot

LL-Q1860 (eng)-Flame, not lame-pseudoroot.wav

This allows one to express coefficients of polynomials in terms of pseudoroots.

2016, Scott Chapman, Marco Fontana, Alfred Geroldinger, Multiplicative Ideal Theory and Factorization Theory, page 398:

(mathematics) A value that appears to be a root of a polynomial equation but that is not actually a root, such as one obtained when factors cancel out in the process of solving the equation.


EGF

exponential generating function
exponential generating function#English

(mathematics) Initialism of exponential generating function.


Brunnian braid

(topology) A braid that becomes trivial upon removal of any one of its strings.


Iwahori-Hecke algebra

Iwahori-Hecke algebra (plural Iwahori-Hecke algebras)

Named for Erich Hecke and Nagayoshi Iwahori.

(mathematics) A deformation of the group algebra of a Coxeter group.


reinforcement learning

Reinforcement learning can be seen as somewhere between supervised and unsupervised learning. The learning system receives a feedback for its actions, but it is not provided with examples to learn from.

2010, Lutz Frommberger, Qualitative Spatial Abstraction in Reinforcement Learning, Springer Science & Business Media, →ISBN, page 10:

Let us look more deeply at reinforcement learning, to see what it means to learn from our own actions. Reinforcement learning is a field in which an agent learns by interacting with an environment.

2022, Aske Plaat, Deep Reinforcement Learning, Springer Nature, →ISBN, page 3:

(machine learning) A type of explorative learning via feedback in a simulated environment.

RLHF

reinforcement learning from human feedback


hyperboloid of revolution

hyperboloid of revolution (plural hyperboloids of revolution)

(geometry) The surface generated by rotating a hyperbola around one of its principal axes.


iterated integral

iterated integral (plural iterated integrals)

(mathematics) In multivariable calculus, the result of applying integrals to a function of more than one variable in such a way that each of the integrals considers some of the variables as given constants.


stochastic parrot

stochastic parrot (plural stochastic parrots)

Coined by American linguist Emily M. Bender in 2021 as a reminder of the limitations of language models, see quotations.

coinage

[…] an LM is a system for haphazardly stitching together sequences of linguistic forms it has observed in its vast training data, according to probabilistic information about how they combine, but without any reference to meaning: a stochastic parrot.

2021 March 3, Emily M. Bender, Timnit Gebru, Angelina McMillan-Major, Shmargaret Shmitchell, “On the Dangers of Stochastic Parrots: Can Language Models Be Too Big? 🦜”, in Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency, ACM, →DOI, →ISBN, pages 610–623:

artificial intelligence
artificial intelligence

(machine learning, derogatory) A language model that uses artificial intelligence to generate seemingly coherent or contextually relevant text but does not truly understand the meaning of the language it is processing


GOFAI

Coined by John Haugeland in his 1985 book Artificial Intelligence: The Very Idea.

artificial intelligence
artificial intelligence#English

Acronym of good old-fashioned artificial intelligence (“a rule-based or logic-based form of symbolic AI”).


Siegel disc

(mathematics) A connected component in the Fatou set where the dynamics is analytically conjugate to an irrational rotation.


Hadjicostas's formula

Riemann zeta function
Riemann zeta function

(mathematics) A formula relating a certain double integral to values of the gamma function and the Riemann zeta function.


Brunn-Minkowski theorem

Developed by Hermann Brunn and Hermann Minkowski.

(mathematics) An inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space.


horizon effect

From the idea that the computer cannot look beyond its horizon (limit of one's knowledge; boundary or threshold).

gloss

(artificial intelligence, games) A problem in artificial intelligence whereby a computer can only search a small portion of the possible states in a game, and thus may make a detrimental move because it cannot search far enough to see its error.


genAI

en-noun

genAI (countable and uncountable, plural genAIs)

At a simple level, this means that the use of genAI requires human oversight. We will seek to use genAI tools editorially only where it contributes to the creation and distribution of original journalism.

2023 June 16, Katharine Viner, Anna Bateson, “The Guardian’s approach to generative AI”, in The Guardian, →ISSN:


Cartesian equation

Cartesian equation (plural Cartesian equations)

(geometry, algebra) An equation that describes a line or plane in terms of the relationship between the coordinates on the axes involved.


VEM

variable entrant map
variable entrant map#English

(mathematics) Initialism of variable entrant map.


multiflow

For vertex-capacitated multiflows the unary case has to be distinguished from vertex-disjoint paths if G is restricted for instance to planar graphs.

2008, Guyslain Naves, András Sebő, “Multiflow Feasibility: An Annotated Tableau”, in William J. Cook, László Lovász, Jens Vygen, editors, Research Trends in Combinatorial Optimization, Berlin: Springer, →ISBN, page 266:

Given that several dependency types flow through the networks, multicommodity flows or multiflows is a natural theoretical framework to map the presented model for further investigations.

2010, Bernhard Hämmerli, Critical Information Infrastructures Security, page 32:

Despite these restricted multiflows, the gap between integer and half-integer flow is at least 1/2 for these graphs […]

2020, Naveen Garg, Nikhil Kumar, András Sebő, “Integer Plane Multiflow Maximisation: Flow-Cut Gap and One-Quarter-Approximation”, in Daniel Bienstock, Giacomo Zambelli, editors, Integer Programming and Combinatorial Optimization: 21st International Conference, IPCO 2020, London, UK, June 8–10, 2020, Proceedings (Lecture Notes in Computer Science; 12125), Cham: Springer Nature, →ISBN, page 148:

(graph theory) A flow function that operates on the set of edges (ordered pairs of vertices) on the intersection of two related directed graphs.


MLOps

Blend of ML (“machine learning”) + DevOps.

blend

The goal of MLOps is to minimize the technical friction to get the model from an idea to production in the shortest possible time with high-quality predictive power and with as little risk as possible.

2021, Hien Luu, Beginning Apache Spark 3, 2nd edition, Apress, →ISBN:

(machine learning) A paradigm that aims to deploy and maintain machine learning models in production reliably and efficiently.


Minkowski-Bouligand dimension

en-noun

Minkowski-Bouligand dimension (plural Minkowski-Bouligand dimensions)

Named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.

(geometry) A way of determining the fractal dimension of a set in a Euclidean space, or more generally in a metric space. It may be visualized by imagining the fractal lying on an evenly-spaced grid and counting how many boxes are required to cover the set. The dimension is then calculated by seeing how this number changes as the grid is made finer.


Auslander-Reiten theory

Introduced by Maurice Auslander and Idun Reiten (1975).

representation theory
representation theory

Auslander-Reiten sequence
Auslander-Reiten sequence

almost split sequence
almost split sequence

Auslander-Reiten quiver
Auslander-Reiten quiver

(algebra) The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers.


almost split sequence

almost split sequence (plural almost split sequences)

Auslander-Reiten sequence
Auslander-Reiten sequence#English

(algebra) Synonym of Auslander-Reiten sequence


Hartley function

(mathematics) A measure of uncertainty. If a sample from a finite set A uniformly at random is picked, the information revealed after the outcome is known is given by the Hartley function H_0(A):=log_b|A|, where |A| denotes the cardinality of A.


Jackson integral

Jackson integral (plural Jackson integrals)

The Jackson integral enjoys several elementary properties of the usual integral.

1993, D. B. Fuks, Unconventional Lie Algebras, page 52:

By taking residues, we can represent this integral in terms of a Jackson integral.

2001, Publications of the Research Institute for Mathematical Sciences, page 72:

We can find elliptic solutions to Yang-Baxter equations as connection functions among Jackson integrals giving asymptotics corresponding to asymptotic regions […]

2012, Simon Gindikin, James Lepowsky, Robert Wilson, Functional Analysis on the Eve of the 21st Century, page 11:

(mathematics) The series expansion ∫₀ᵃf(x),rm d_qx=(1-q),a∑ₖ₌₀ ᪲qᵏf(qᵏa). for real variable a and function of a real variable f(x).


Weingarten equation

Weingarten equation (plural Weingarten equations)

They were established in 1861 by the German mathematician Julius Weingarten.

(mathematics) Any of a group of equations giving the expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of a point on the surface.


GOL

Alternative form: GoL

Any info about optimal GOL-algorithms are also welcome. The algorithm I figured is quite fast, but certainly not optimal.. I am using 320x198 (=63360) array of cells, and with my machine I am getting about 7.7 generations per second, but with some assembly optimizing I could be even faster.

1993 September 7, Teemu Lahteenmaki, “Game of Life patterns wanted”, in comp.theory.cell-automata (Usenet):

Can someone please tell me if/where there is a central repository or web site to which GoL pattern files may be posted? I have been doing some modest engineering/artwork in GoL that I wud like 2 share with others.

2003 September 22, Otis Schmakel, “File Posting Place(s)”, in comp.theory.cell-automata (Usenet):

Let's count a number of rules that can be built in GoL-like automatas.

2021 October 19, Stefan W., “Game of Life with real 8 neighbors”, in comp.theory.cell-automata (Usenet):

(cellular automata) Initialism of Game of Life.


GoL

Alternative form: GOL


glide reflection

glide reflection (countable and uncountable, plural glide reflections)

Thus every function of the form eⁱᵃz + c is the composition of a translation with a reflection and so it is a glide reflection.

1993, Saul Stahl, The Poincaré Half-plane: A Gateway to Modern Geometry, Jones & Bartlett Learning, →ISBN, page 136:

That turns out to have one small spaceship, moving diagonally up and left at c/14 with period 14 (glide reflection at generation 7):

1995 November 12, Rich Holmes, “Totalistic spaceships”, in comp.theory.cell-automata (Usenet):

Footprints along a line have glide reflection symmetry.

2004, Dorothy Koster Washburn, Donald W. Crowe, Donald Warren Crowe, Symmetry Comes of Age: The Role of Pattern in Culture, University of Washington Press, →ISBN, page 6:

(geometry) A transformation consisting of a reflection followed by a translation along the same line.


puffer train

The commonest use of sparks from these spaceships is to perturb an "engine" to produce puffer trains, or to modify stationary objects when the spaceships pass by.

1992 August 13, David Bell, “Spaceships in Conway's Life (Part 1)”, in comp.theory.cell-automata (Usenet):

The second has speed c/2, period 2. This one also works in B3/S035; the first is no longer a spaceship but a minimalist puffer train, leaving behind a trail of isolated cells!

I stuck the rule and seed into Golly, and after a few tens of thousands of generations, stuck another seed in such that the arms of gliders spewed by the two blobs would intersect, and without any more planning than that, it constructed a puffer train, that survived ten or twelve major pattern replications despite the sleet of gliders colliding with it, before it finally got clobbered hard enough to disrupt its progress.

2007 June 3, Kent Dolan, “A "new" Conway Life experience.”, in comp.theory.cell-automata (Usenet):


outer totalistic

Why it is important, to design totalistic or outer totalistic rules?

2003 January 18, Frank Buss, “Searching detailed description of Codd's automaton”, in comp.theory.cell-automata (Usenet):

It's the second-order reversible outer totalistic rule b1234/s0123R on the von Neumann neighborhood.

2003 December 13, Ilmari Karonen, “'TimeWarp' CA rule -- anyone recognize this one?”, in comp.theory.cell-automata (Usenet):

Hello, How to compute lambda value for (outer-)totalistic rule? Is it the same way like computing for elementary?

2007 August 28, Bob, “Lambda value of (outer-)totalistic code”, in comp.theory.cell-automata (Usenet):

(cellular automata) Having the state of each cell represented by a number, and the value of a cell dependent only on its current value along with the sum of the values of nearby cells.


Life-like cellular automaton

Life-like cellular automaton (plural Life-like cellular automata or Life-like cellular automatons)

Life-like cellular automata (plural)
Life-like cellular automatons (plural)

(cellular automata) A cellular automaton resembling Conway's Game of Life in terms of its ruleset (i.e. 2D, binary, outer totalistic, and using the Moore neighborhood).


von Neumann neighborhood

von Neumann neighborhood (plural von Neumann neighborhoods)

Named after John von Neumann, Hungarian mathematician.

(cellular automata) A neighborhood on a 2D square lattice consisting of a cell and its four orthogonal neighbors.

John von Neumann
von Neumann neighborhood


Moore neighborhood

Moore neighborhood (plural Moore neighborhoods)

For Edward F. Moore, American cellular automatist

(cellular automata) A neighborhood on a 2D square lattice consisting of a cell and its eight orthogonal and diagonal neighbors.


Life without Death

Named for the fact that the birth rules are identical to those of the Game of Life, but the survival rules are such that it is impossible for living cells to die.

Life-like cellular automaton
Life-like cellular automaton

(cellular automata) A Life-like cellular automaton with the rule B3/S012345678.


Highlife

(cellular automata) A Life-like cellular automaton with the rule B36/S23.


Day and Night

Named for the fact that the rule is its own complement; toggling all cell states results in the pattern evolving similarly, but with living and dead cells switched.

(cellular automata) A Life-like cellular automaton with the rule B3678/S34678.


dragonlength

Further investigation proved that the plateau was isolated and ample to pasture a huge herd of food[-]beasts for the dragons. It ended in a sheer drop of several dragonlengths into denser jungle on one side, the sea-side escarpment on the other.

1968, Anne McCaffrey, “The Cold Between”, in Dragonflight, Ballantine Books, published 1974, →ISBN, page 262:

An elv’in scoutship was not a large ship, less than two dragonlengths.

2002, James Clemens (pseudonym; James Paul Czajkowski), Wit’ch Star, New York, N.Y.: Del Rey Books, →ISBN, page 28:

The Copper stood before the massive Black Rock in the center of the Lavadome; it was dozens of dragonlengths high, heavy and black and forbidding.

2007, E. E. Knight (pseudonym; Eric Frisch), chapter 22, in Dragon Outcast (The Age of Fire; 3), Roc Books, →ISBN, page 257:

(fantasy) A distance equal to the length of a dragon.


Riemann-Roch theorem

Initially proven by Bernhard Riemann (1857); further work was done by Riemann's student Gustav Roch (1865).

(mathematics) An important theorem in complex analysis and algebraic geometry for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles.


Sperner family

Sperner family (plural Sperner families)

(combinatorics) A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice over the power set of E.


Jackson derivative

Jackson derivative (plural Jackson derivatives)

(mathematics) A q-analog of the ordinary derivative.


q-derivative

Jackson derivative
Jackson derivative#English

(mathematics) Synonym of Jackson derivative


tree kernel

(machine learning) A tree data structure based on the more general concept of the positive-definite kernel, used in the parsing and classification of sentences.


pseudoreflexive

LL-Q1860 (eng)-Flame, not lame-pseudoreflexive.wav

In the next two theorems we will assume E pseudoreflexive. This is not a big restriction since every Banach space over a spherically complete nonarchimedean field is pseudoreflexive.

2001, José N. Aguayo, Thomas E. Gilsdorf, “Non-Archimedean Vector Measures and Integral Operators”, in A. K. Katsaras, W. H. Schikhof, L. Van Hamme, editors, p-adic Functional Analysis: Proceedings of the Sixth International Conference (Lecture Notes in Pure and Applied Mathematics), New York, NY: Marcel Dekker, Inc., →ISBN, page 8:

(mathematics) Inducing a topological isomorphism between the domain and its image.


Stern-Brocot tree

Stern-Brocot tree (plural Stern-Brocot trees)

Introduced independently by Moritz Stern (1858) and Achille Brocot (1861).

(number theory) An infinite complete binary tree whose vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.


Kazhdan-Margulis theorem

the Kazhdan-Margulis theorem (canonical)

Proven in the 1960s by David Kazhdan and Grigory Margulis.

(mathematics) A statement asserting that a discrete subgroup in semisimple Lie groups cannot be too dense in the group. More precisely, in any such Lie group there is a uniform neighborhood of the identity element such that every lattice in the group has a conjugate whose intersection with this neighborhood contains only the identity.


Ramanujan-Petersson conjecture

the Ramanujan-Petersson conjecture (canonical)

Named after Srinivasa Ramanujan and Hans Petersson.

Ramanujan conjecture
Ramanujan conjecture

(mathematics) A generalization of the Ramanujan conjecture to other modular forms or automorphic forms.


Ramanujan conjecture

Ramanujan tau function
Ramanujan tau function

(mathematics) A conjecture stating that the Ramanujan tau function given by the Fourier coefficients τ(n) of the cusp form Δ(z) of weight 12 Δ(z)=∑_(n>0)τ(n)qⁿ=q∏_(n>0)(1-qⁿ)²⁴=q-24q²+252q³-1472q⁴+4830q⁵-⋯, where q=e^(2πiz), satisfies |τ(p)|≤2p^(11/2), when p is a prime number.


Ramanujan graph

Ramanujan graph (plural Ramanujan graphs)

Named after mathematician Srinivasa Ramanujan.

(graph theory) A regular graph whose spectral gap is almost as large as possible, making it an excellent spectral expander. Such graphs are relevant to diverse branches of pure mathematics.


Margulis lemma

differential geometry
differential geometry

(differential geometry) A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold.


Petersson inner product

Petersson inner product (plural Petersson inner products)

It was introduced by the German mathematician Hans Petersson.

(mathematics) An inner product defined on the space of entire modular forms.


data poisoning

data poisoning (countable and uncountable, plural data poisonings)

While data sanitization shows promise to defend against data poisoning, it is often impossible to validate every data source [14].

2019, Simon N. Foley, editor, Data and Applications Security and Privacy XXXIII […] , Springer, →ISBN, page 4:

Similarly, the Tay chatbot suffered from data poisoning. To mitigate data poisoning, it is important not to let any one group contribute too much data to a model.

2022, Alfred Z. Spector, Peter Norvig, Chris Wiggins, Jeannette M. Wing, Data Science in Context: Foundations, Challenges, Opportunities, Cambridge University Press, →ISBN, page 148:

Data poisoning is one type of adversarial attack—where a user or group of users submit false data to influence the model toward a particular or incorrect prediction.

2023, Katharine Jarmul, Practical Data Privacy, O'Reilly, →ISBN:

Some forms of data poisoning are undetectable. Attackers can insert adversarial noise into the training data, altering the training data in a way that is hidden to human observers.

2023, Paul Scharre, Four Battlegrounds: Power in the Age of Artificial Intelligence, W. W. Norton & Company, →ISBN:

(machine learning, computer security) The deliberate use of a training dataset with data designed to increase errors in the output of a machine learning model.

machine learning; computer security; machine learning; computer security


poisoning attack

poisoning attack (plural poisoning attacks)

Just like how you can poison a village by poisoning its water source, poisoning attacks corrupt the AI system from functioning by poisoning the input data.

2023, Ram Shankar Siva Kumar, Hyrum Anderson, Not with a Bug, But with a Sticker […] , John Wiley & Sons, →ISBN:

(machine learning, computer security) Synonym of data poisoning


SNARG

2018, Dan Boneh, Yuval Ishai, Amit Sahai, David J. Wu, Quasi-Optimal SNARGs via Linear Multi-Prover Interactive Proofs, Jesper Buus Nielsen, Vincent Rijmen (editors), Advances in Cryptology – EUROCRYPT 2018: 37th Annual International Conference on Cryptographic Techniques, Proceedings, Part III, Springer, LNCS 10822, page 224,
A SNARG is publicly verifiable if anyone can verify the proofs, and it is designated-verifier if only the holder of a secret verification state (generated along with the CRS) can verify proofs.

However, SNARGs and SNARKs (blockchain implementations of SNARGs) rely on pre-quantum assumptions and are not post-quantum secure. Hence, lattice-based SNARGs are proposed (Boneh et al., 2017).

2020, Melanie Swan, Renato P Dos Santos, Frank Witte, Quantum Computing, World Scientific, page 172:

2021, Yael Taumann Kalai, Vinod Vaikuntanathan, Rachel Yun Zhang, Somewhere Statistical Soundness, Post-Quantum Security, and SNARGs, Kobbi Nissim, Brent Waters (editors), Theory of Cryptography: 19th International Conference, TCC 2021, Proceedings, Part I, Springer, LNCS 13042, page 355,
In this section, we construct SNARGs for languages with a (computational) non-signaling mathsf PCP, assuming the existence of a SNARG for mathsf BatchNP.

(computing, cryptography) Acronym of succinct non-interactive argument.


SNARK

2019, Anca Nitulescu, Lattice-Based Zero-Knowledge SNARGs for Arithmetic Circuits, Peter Schwabe, Nicolas Thériault (editors), Progress in Cryptology – LATINCRYPT 2019: 6th International Conference, Proceedings, Springer, LNCS 11774, page 223,
SNARG vs. SNARK. If we replace the computational soundness with computational Knowledge Soundness we obtain what we call a SNARK, a succinct non-interactive argument of knowledge.

2020, Fuyuki Kitagawa, Takahiro Matsuda, Takashi Yamakawa, NIZK from SNARG, Rafael Pass, Krzysztof Pietrzak (editors), Theory of Cryptography: 18th International Conference, Proceedings, Part I, Springer, LNCS 12550, page 568,
Actually, what is often used in blockchains is a SNARK [4], which is a stronger variant of a SNARG that satisfies extractability.

2023, Matteo Campanelli, Chaya Ganesh, Hamidreza Khoshakhlagh, Janno Siim, Impossibilities in Succinct Arguments: Black-Box Extraction and More, Nadia El Mrabet, Luca De Feo, Sylvain Duquesne (editors), Progress in Cryptology - AFRICACRYPT 2023: 14th International Conference, Proceedings, Springer, LNCS 14064, page 467,
Whether we can build SNARKs with black-box extraction in the standard model is an elusive problem. […] In particular, we show that a SNARG can be lifted to a SNARK with the features above for the class of languages FewP (roughly, NP with polynomial many witnesses).

succinct non-interactive argument of knowledge#English

(computing, cryptography) Acronym of succinct non-interactive argument of knowledge.


if-thenism

We now come to the difficulty that caused Russell himself to abandon 'if-thenism'.

1968, Bertrand Russell; philosopher of the century, page 287:

In this chapter we shall consider two versions of if-thenism corresponding to two different ways of understanding conditional statements.

1979, Introduction to the philosophy of mathematics, page 11:

The final formalist position we shall consider, deductivism, or if-thenism as it is sometimes called, is suggested by earlier remarks on the game of pure logic.

1994, Understanding the infinite, page 185:

(mathematics) The doctrine that all mathematical statements are conditional in form, meaning they can be expressed in the format "p implies q", (i.e. if p then q).


bifid cipher

Coordinate term: trifid cipher

(cryptography) A classical cipher that combines the Polybius square with transposition, and uses fractionation to achieve diffusion.


trifid cipher

Coordinate term: bifid cipher

(cryptography) A classical cipher that extends the earlier bifid cipher with the use of trigrams.


ronnameter

The observable universe is about one ronnameter in diameter.

An electron’s mass is about one rontogram, Jupiter weighs two quettagrams and the diameter of the observable universe is one ronnameter.

2022 November 23, Katrina Krämer, “SI units get new prefixes for huge and tiny numbers”, in Chemistry World:


ronnasecond

(metrology) An SI unit of time equal to 10²⁷ seconds. Symbol: Rs


Caesar substitution

Caesar substitution (countable and uncountable, plural Caesar substitutions)


Arakelov

Borrowed from Russian Араке́лов (Arakélov), a Russified form of Armenian Առաքելյան (Aṙakʻelyan).

(mathematics, used attributively) Soviet-Armenian mathematician Suren Arakelov.


coordinate plane

coordinate plane (plural coordinate planes)

(mathematics) A Euclidean plane with a system of coordinates.


exaparsec

(astronomy) An astronomical unit of distance equal to 10¹⁸ parsecs.


Desargues's theorem

(geometry) A theorem stating that two triangles are in perspective axially if and only if they are in perspective centrally.