shearlet

(mathematics) An extension of the wavelet, allowing the efficient encoding of anisotropic features in multivariate problem classes.


monoliteral

(cryptography) That uses a single letter as a cipher


multinormal

This was done for each population separately by randomizing the simulated values from a multinormal distribution with the following parameters: the 14 observed means characteristic of the given population, and as variance the average of the 7 geometric means of the 14 variances per population.

2015 July 21, “Once upon Multivariate Analyses: When They Tell Several Stories about Biological Evolution”, in PLOS ONE, →DOI:

(statistics, of a distribution) multivariate and normal


MANCOVA

(statistics) Acronym of multivariate analysis of covariance: an extension of ANOVA methods to cover cases where there is more than one dependent variable and where the control of covariates is required.


JOI

orbital insertion
orbital insertion#English

(astronautics) Initialism of Jupiter orbital insertion.


HDA

en-noun

HDA (countable and uncountable, plural HDAs)

(algebra) Initialism of higher-dimensional algebra.


dismantlability

(chiefly graph theory) The quality of being dismantlable.


dismantlable

(set theory) The property of an ordered set such that its elements can be listed in an order such that, for every element, the element is irreducible (has exactly one upper or lower cover) in the subset consisting of that element and all subsequent elements.

We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere.

2015, Michal Adamaszek, “A note on independence complexes of chordal graphs and dismantling”, in arXiv:

(graph theory) The property of a graph such that its vertices can be listed in an order such that, for every vertex, the vertex is a subdominant vertex (has an adjacent vertex that is adjacent to every other vertex that it is adjacent to) in the induced subgraph generated by that vertex and all subsequent vertices.


minorize

en-verb

minorize (third-person singular simple present minorizes, present participle minorizing, simple past and past participle minorized)

minorizes (present singular third-person)
minorizing (participle present)
minorized (participle past)
minorized (past)

(mathematics) To be or become a lower bound


Iitaka dimension

en-noun

Iitaka dimension (plural Iitaka dimensions)

(algebraic geometry) The Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L.


monohedral

(mathematics, of a tessellation) Having exactly one prototile.


softmax

Coined by John S. Bridle in 1989, on the grounds of the function being "a differentiable generalisation of the 'winner-take-all' operation of picking the maximum value".

(mathematics, statistics) A generalization of the logistic function that "squashes" a K-dimensional vector mathbf z of arbitrary real values to a K-dimensional vector σ( mathbf z) of real values in the range (0, 1).


base year

(statistics, economics) a year chosen for comparison with other years, in statistical analysis and various indices, such as a price index. It usually has an arbitrary value of 100 to make percentage comparisons easier. A new base year can be chosen as the years progress.


pluperfection

pluperfection (usually uncountable, plural pluperfections)

(mathematics) Property of a certain category of graphs.


pseudofunctor

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

(mathematics) A mapping between categories that is just like a functor except that f(x∘y)=f(x)∘f(y) and f(1)=1 do not hold as exact equalities but only up to coherent isomorphisms.


quandle

Coined by David Joyce in his 1982 paper A classifying invariant of knots: the knot quandle.

(mathematics) A rack, scriptstyle Q,, such that scriptstyle ∀a;∈;Q a triangleright a=a or equivalently a triangleleft a=a.


changepoint

This allows both documented and undocumented changepoints to be analyzed in tandem.

2015, Yingbo Li, Robert Lund, Hewa A. Priyadarshani, “Bayesian Minimal Description Lengths for Multiple Changepoint Detection”, in arXiv:

probability distribution
probability distribution

(statistics) The point at which the probability distribution of a stochastic process or time series changes.


nullcline

ordinary differential equation
ordinary differential equation

(mathematics) A zero-growth isocline, encountered in a system of ordinary differential equations.


bicompletion

(mathematics) The process that makes a category bicomplete.


autoreducibility

Finally, we consider autoreducibility for ITRMs and show that randomness implies non-autoreducibility..

2015, Merlin Carl, “Randomness and Degree Theory for Infinite Time Register Machines”, in arXiv:

(mathematics, set theory) The state or quality of being autoreducible.


autoreducible

(mathematics, set theory) Of a set, that can be reduced to itself by a Turing machine that does not ask for its own input.


eigenarray

1999, O. Alter et al., ‘‘Singular Value Decomposition for Gene Expression Data Processing and Modeling.’’ In: After the Genome V (December 6–10, 1999, Jackson Hole, WY).
We describe the use of singular value decomposition in transforming gene expression data from genes/arrays space to ‘‘eigengenes’’/‘‘eigenarrays’’ space, where the eigengenes and eigenarrays are unique orthonormal superpositions of the genes and arrays, respectively.

2000, O. Alter et al., ‘‘Singular value decomposition for genome-wide expression data processing and modeling,’’ Proc. Natl. Acad. Sci. USA 97 (18), pp. 10101–10106. doi:10.1073/pnas.97.18.10101.
After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

2002, T. O. Nielsen et al., ‘‘Molecular Characterisation of Soft Tissue Tumours: a Gene Expression Study,’’ Lancet 359 (9314), pp. 1301–1307. doi: 10.1016/S0140-6736(02)08270-3.
The separation of the calponin-positive leiomyosarcoma subgroup from the calponin-negative tumours was dominant, and resulted in an important eigengene and corresponding eigenarray.

2006, C. M. Li and R. R. Klevecz, ‘‘A rapid genome-scale response of the transcriptional oscillator to perturbation reveals a period-doubling path to phenotypic change,’’ Proc. Natl. Acad. Sci. USA 103 (44), pp. 16254–16259. doi: 10.1073/pnas.0604860103.
A reconstruction of the attractor can be seen in the plot of the principal eigengenes 2, 3, and 4.

2008, A. Y. Gracey et al., ‘‘Rhythms of Gene Expression in a Fluctuating Intertidal Environment,’’ Curr. Biol. 18 (19), pp. 1501-1507. doi: 10.1016/j.cub.2008.08.049.
Significantly correlated with the first eigengene were GO terms that we classified as being broadly associated with ‘‘metabolism’’ because this cluster was enriched for genes involved in the tricarboxylic acid cycle (TCA), the electron transport chain, metabolism, ATP synthesis, and protein degradation.

2012, M. J. Hawrylycz et al., ‘‘An anatomically comprehensive atlas of the adult human brain transcriptome,’’ Nature 489 (7416), pp. 391–399. doi: 10.1038/nature11405.
Each module is represented by an ‘eigengene’ corresponding to its expression pattern across structures (first left singular vector of the gene × structure matrix), and genes highly correlated with the module eigengene are called ‘hub’ genes.

2013, J. L. Padilla-Gamiño et al., ‘‘Temperature and CO₂ additively regulate physiology, morphology and genomic responses of larval sea urchins, Strongylocentrotus purpuratus’’ Proc. R. Soc. B Biol. Sci. 280 (1759), article 20130155. doi: 10.1098/rspb.2013.0155.
Our gene expression data also indicate that the cystoskeleton is sensitive to shifts in temperature and pCO₂: genes encoding fundamental components of the cellular cytoskeleton such as actin and alpha and beta tubulins were upregulated under elevated temperature, but downregulated under elevated pCO₂ (eigengene 1).

2014, J. M. Tennessen et al., ‘‘Coordinated metabolic transitions during Drosophila embryogenesis and the onset of aerobic glycolysis’’ G3:Genes|Genomes|Genetics 4 (5), pp. 839–850. doi: 10.1534/g3.114.010652.
The second most significant pattern identified by SVD corresponds to broad upregulation of gene expression midway through embryogenesis and is strikingly similar to the coordinate induction of glycolytic genes that defines the embryonic metabolic transition (EmbMT) (eigengene pattern 2).

2020, O. Alter, ‘‘Discovering Genome-Scale Predictors of Survival and Response to Treatment with Multi-Tensor Decompositions’’ 2020 American Association for Cancer Research (AACR) Virtual Annual Meeting II (June 22–24, 2020); YouTube video.
The SVD finds for us patterns that look like genes, which is the eigengene concept which we invented.

(genetics) (mathematics) One of a set of left singular vectors of a genes x samples matrix that tabulates, e.g., the mRNA or gene expression of the genes across the samples, where the samples were assayed by using DNA microarrays. The corresponding right singular vector is the corresponding eigengene.


eigenmatrix

(mathematics, rare) The counterpart of eigenvectors for operators over spaces of matrices.


subtournament

(graph theory) A tournament that forms part of another tournament.


hyperstability

(mathematics) The condition of a system in which there exist two constants k_1>0,k_2>0 such that any state trajectory of the system satisfies the inequality: ‖x(t)‖0


slimplectic

We discuss several example systems, including damped harmonic oscillators, Poynting-Robertson drag, and gravitational radiation reaction, by utilizing our new publicly available code to demonstrate the slimplectic integrator algorithm.

2015, David Tsang, Chad R. Galley, Leo C. Stein, Alec Turner, “Slimplectic Integrators: Variational Integrators for General Nonconservative Systems”, in arXiv:

(mathematics) symplectic in a more generalised manner


KAM

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:

Kolmogorov-Arnold-Moser theorem
Kolmogorov-Arnold-Moser theorem#English

(mathematics) Initialism of Kolmogorov-Arnold-Moser theorem.


polydisc

(mathematics) A Cartesian product of discs.


sparsistency

Its implementation can be done with available packages under a variety of models and, in the linear regression model, we show it is sparsistent under conditions similar to those ensuring sparsistency for an oracular version of the reference stratum strategy.

2015, Edouard Ollier, Vivian Viallon, “Regression modeling on stratified data: automatic and covariate-specific selection of the reference stratum with simple L_1-norm penalties”, in arXiv:

(statistics) Let mathbf b be a vector and define the support operatorname supp( mathbf b)=i: mathbf bᵢ≠0 where mathbf bᵢ is the ith element of mathbf b. Let ̂mathbf b be an estimator for mathbf b. Then sparsistency is the property that the support of the estimator converges to the true support as the number of samples grows to infinity.


cryptoviral extortion

(cryptography, computer security, Internet) A data kidnapping attack studied in the field of cryptovirology, in which malware encrypts user data and asks for payment in exchange for the decryption key.


cryptoviral

(cryptography, computer security) related to a cryptovirus


biquandle

We provide examples demonstrating that the new invariants are not determined by the biquandle counting invariant, the knot quandle, the knot group or the traditional skein invariants..

2015, Sam Nelson, Michael E. Orrison, Veronica Rivera, “Quantum Enhancements and Biquandle Brackets”, in arXiv:

(mathematics) A generalisation of a quandle that is a form of a birack


nonsummable

We show that despite the absence of a spectral gap for all #92;alpha#92;in(0,1) and despite nonsummable correlations for #92;alpha#92;geq 1#47;2, the map #92;alpha#92;mapsto#92;int#92;varphi#92;,d#92;nu#95;#92;alpha is continuously differentiable for #92;varphi#92;inL#123;q#125;#91;0,1#93; for q sufficiently large..

2015, Alexey Korepanov, “Linear response for intermittent maps with summable and nonsummable decay of correlations”, in arXiv:


stacky

(mathematics) Relating to stacks (generalizations of schemes and sheaves).


isocrystal

(algebraic geometry) A kind of p-adic analogue of a sheaf.


Carlyle circle

The idea of using such a circle to solve a quadratic equation is attributed to Thomas Carlyle (1795–1881).

Carlyle circles have been used to develop ruler-and-compass constructions of regular polygons.

(mathematics) A certain circle in a coordinate plane associated with a quadratic equation, having the property that the solutions of the equation are the horizontal coordinates of the intersections of the circle with the horizontal axis.


Fano plane

Named after Gino Fano (1871–1952), an Italian mathematician.

(geometry) The finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point.


quasisymmetric

(mathematics) Almost but not quite symmetric.


Bruck-Ryser-Chowla theorem

Named after Richard Bruck, H. J. Ryser, and Sarvadaman Chowla.

Diophantine equation
Diophantine equation

(mathematics) A result on the combinatorics of block designs, stating that, if a (v, b, r, k, λ)-design exists with v = b (a symmetric block design), then: (i) if v is even, then k − λ is a square; (ii) if v is odd, then the following Diophantine equation has a nontrivial solution: x² − (k − λ)y² − (−1)^((v−1)/2) λ z² = 0.


block design

(mathematics) In combinatorial mathematics, a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties deemed useful for a particular application.


monomialize

en-verb

monomialize (third-person singular simple present monomializes, present participle monomializing, simple past and past participle monomialized)

monomializes (present singular third-person)
monomializing (participle present)
monomialized (participle past)
monomialized (past)

(mathematics, transitive) To make into a monomial


trigonometrist

During his next visit, very proud of herself, the young trigonometrist began to speak about the book to its author.

2011, Michele Audin, Remembering Sofya Kovalevskaya, Springer Science & Business Media, page 34:

(mathematics) One who does trigonometry.


TP

en-noun

TP (countable and uncountable, plural TPs)

transportation problem
transportation problem#English

(mathematics) Initialism of transportation problem.


semisymmetrization

A new semisymmetrization functor, which maps the category of quasigroups with homotopies to the category of semisymmetric quasigroups with homomorphisms is given.

2015, Aleksandar Krapez, Zoran Petric, “A note on semisymmetry”, in arXiv:

(mathematics) The act or process of making semisymmetric


eigenratio

By tuning the weights of any given network so as to reach the lowest possible eigenratio #92;lambda#95;N#47;#92;lambda#95;2, the synchronized state is guaranteed to be maintained across the longest possible range of coupling strengths.

2015, R. Sevilla-Escoboza, J. M. Buldú, S. Boccaletti, D. Papo, D.-U. Hwang, G. Huerta-Cuellar, R. Gutiérrez, “Experimental implementation of maximally synchronizable networks”, in arXiv:


posheaf

We also give characterizations of continuous posheaves and completely distributive posheaves, and show that an algebraic completely distributive posheaf is spatial.

2015, Wei He, “Partially Ordered Sheaves on a Locale. I (II)”, in arXiv:


multiquadric

To avoid this disadvantage of spatial distance measurement, we herein describe each object (e.g. cell nucleus) by a scalar field on the basis of an inverse multiquadric radial basis function.

2015 September 2, Cleo-Aron Weis et al., “On the representation of cells in bone marrow pathology by a scalar field: propagation through serial sections, co-localization and spatial interaction analysis”, in Diagnostic Pathology, volume 10, →DOI:

(mathematics) Being a Radial basis function of the form ϕ(r)=√.


Ricci calculus

Named after Gregorio Ricci-Curbastro, who developed the notation and theory in the late 19th century.

1945 [McGraw-Hill, 2nd Edition], E. T. Bell, The Development of Mathematics, Dover, 1992, page 357,
The method of calculation is the absolute differential calculus, or tensor analysis, of M. M. G. Ricci (1853–1925, Italian), which was noted earlier in connection with the general progress of recent mathematics toward structure. The Ricci calculus, however, originated in the algebra of quadratic differential forms. […] The Ricci calculus did not come into its own geometrically until it was publicized by the relativists, when the geometers adopted and further developed it.

This structure, we suggest, will show more clearly when examined in the language of geometry rather than in the language of differential equations, more readily in Regge calculus than in Ricci calculus, and more directly from a geometry idealized to be blockwise flat than from functions idealized to be piecewise linear.

1986, Warner Allen Miller, “Geometric Computation: Null-Strut Geometrodynamics and the Inchworm Algorithm”, in Joan M. Centrella, editor, Dynamical Spacetimes and Numerical Relativity, Cambridge University Press, page 256:

The absolute differential calculus is also known as tensor calculus or Ricci calculus. Its development was mainly due to Gregorio Ricci Curbastro (1853-1925) who elaborated the theory during the ten years 1887-1S96.

1995, Ignazio Ciufolini, John Archibald Wheeler, John Wheeler, Gravitation and Inertia, Princeton University Press, page 19:

(mathematics) A formal system in which index notation is used to define tensors and tensor fields and the rules for their manipulation; the theory of tensor calculus as developed by Gregorio Ricci-Curbastro, which formed the foundation of the modern theory.


polyserial

We analyzed the psychometric properties of ABCR-14 according to entropy, polyserial correlation coefficient, exploratory factor analysis, confirmatory factor analysis, average variance extracted, Cronbach’s alpha, Pearson product-moment correlation coefficient, and multidimensional item response theory (MIRT).

2015 August 7, “Development of the Assessment of Belief Conflict in Relationship-14 (ABCR-14)”, in PLOS ONE, →DOI:

(statistics) Relating to the correlation between multiple continuous variables


hypersimplex

hypersimplex (plural hypersimplexes or hypersimplices)

hypersimplexes (plural)
hypersimplices (plural)

(mathematics) A kind of convex polytope that generalizes the simplex, defined as the convex hull of a d-dimensional vector whose coefficients consist of k ones and d−k zeros.


mirabolic

We also give an analogue of our main theorem in the setting of mirabolic D-modules.

2015, Gwyn Bellamy, Travis Schedler, “Kostka polynomials from nilpotent cones and Springer fiber cohomology”, in arXiv:

(mathematics) Being or relating to a subgroup of the general linear group GLₙ(k) that consists of automorphisms fixing a given non-zero vector in kⁿ. Its image in the projective general linear group is a parabolic subgroup consisting of all elements fixing a given point of projective space.


semistandard

In the Grassmannian case, a prism tableau with colors ignored is a semistandard Young tableau.

2015, Anna Weigandt, Alexander Yong, “The Prism tableau model for Schubert polynomials”, in arXiv:

(mathematics) Of a Young tableau: having the entries weakly increasing along each row and strictly increasing down each column.


subcontinuum

subcontinuum (plural subcontinua or (rare) subcontinuums)

subcontinua (plural)
subcontinuums (plural rare)

(mathematics) A continuum making up part of another continuum.


Hopfian

(mathematics) Relating to, or introduced by, Heinz Hopf (1894–1971), German mathematician.


quasianalytic

(mathematics) Belonging or relating to a generalization of the class of real analytic functions based upon the fact that, if f is an analytic function on an interval [a,b] ⊂ R, and at some point f and all of its derivatives are zero, then f is identically zero on all of [a,b].


semimodule

(mathematics) A mathematical construct that resembles a module, except that the underlying abelian group is replaced with an abelian semigroup, so the elements do not necessarily have inverses.


Dickman function

(number theory) A function, denoted by ρ, used to estimate the proportion of smooth numbers up to a given bound.


linearoid

In this case, therefore, the linearoid system of invariant differential equations is merely the linearoid transform of a linear system.

(mathematics) (in group theory) quasi-linear


Catalan surface

Catalan surface (plural Catalan surfaces)

Named after the Belgian mathematician Eugène Charles Catalan.

(geometry) A ruled surface whose rulings are all parallel to a fixed plane.


lineoid

From line + -oid, from Latin linea (“line”).

(mathematics, dated) the set of points in 3-dimensional space that are also points in 4-dimensional space


bithreshold

The threshold, bithreshold, and nor functions of Eqs (1 ), (2 ), and (3 ) are three such types.

2015 August 12, “GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems”, in PLOS ONE, →DOI:

(mathematics) The intersection of two thresholds


ultrametricize

en-verb

ultrametricize (third-person singular simple present ultrametricizes, present participle ultrametricizing, simple past and past participle ultrametricized)

ultrametricizes (present singular third-person)
ultrametricizing (participle present)
ultrametricized (participle past)
ultrametricized (past)

As no branch length information was available, we determined the most appropriate transformation to ultrametricize the tree correlating the absolute values of the standardized contrasts of ln brain size vs. the square root of the sum of the corrected branch lengths in PDAP/PDTree [67 ] in Mesquite 2.75 [68 ].

2015 August 12, “Relative Brain and Brain Part Sizes Provide Only Limited Evidence that Machiavellian Behaviour in Cleaner Wrasse Is Cognitively Demanding”, in PLOS ONE, →DOI:


hyperpath

(mathematics) Any path that is longer than the shortest path possible


isoelastic

For the class of isoelastic functions that we address in this paper, it is still possible to derive a closed expression for the value of the firm.

2015, Cláudia Nunes, Rita Pimentel, “Optimal stopping times in jump processes”, in arXiv:

(mathematics) Exhibiting a constant elasticity.


pseudovariety

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

Pseudovarieties are of particular importance in the study of finite semigroups and hence in formal language theory.

(mathematics) A class of algebras of a given signature, closed under the taking of homomorphic images, subalgebras and finitary direct products.


copositive

(mathematics) Of a real matrix A: such that xᵀᴬˣ≥0 for every non-negative vector x≥0.


coatomistic

(mathematics) Of a set: such that every element is the greatest lower bound of a set of coatoms.


pseudoring

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

(mathematics) Any of various variants of a ring.


needle-shaped

en-adj

needle-shaped (comparative more needle-shaped, superlative most needle-shaped)

more needle-shaped (comparative)
most needle-shaped (superlative)


cotree

(mathematics) A tree that defines a cograph, its leaves corresponding to the nodes of the cograph.


divisorial

An important piece of information in the theory of the arithmetic Galois action on the geometric fundamental groups of schemes is that divisorial inertia is acted on cyclotomically.

2015, Filippo Callegaro, Giovanni Gaiffi, Pierre Lochak, “Garside elements, inertia and Galois action on braid groups”, in arXiv:


fibral

The structure of such couplings is unraveled by exploiting the perturbative and non-perturbative homological relations, introduced in our companion paper arXiv:1506.06764, which encode the interplay between the self-dual 3-form flux on the M5-brane, the background 4-form flux and certain fibral curves.

2015, Luca Martucci, Timo Weigand, “Hidden Selection Rules, M5-instantons and Fluxes in F-theory”, in arXiv:

(especially mathematics) Having the form of a fiber or fibril


fibrant

This means that the fibrant replacement functor does not preserve the causal structure.

2015, Philippe Gaucher, “About the choice of cofibrations of higher dimensional transition systems”, in arXiv:


framelet

Such symmetric quincunx tight framelets are associated with quincunx tight framelet filter banks #92;#123;a#59;b#95;1,b#95;2,b#95;3#92;#125; having increasing orders of vanishing moments and enjoying the additional double canonical properties: b#95;1(k#95;1,k#95;2)#61;(-1)#123;1#43;k#95;1#43;k#95;2#125;a(1-k#95;1,-k#95;2),b#95;3(k#95;1,k#95;2)#61;(-1)#123;1#43;k#95;1#43;k#95;2#125;b#95;2(1-k#95;1,-k#95;2). For a low-pass filter a which is not a quincunx orthonormal wavelet filter, we show that a quincunx tight framelet filter bank #92;#123;a#59;b#95;1,#92;ldots,b#95;L#92;#125; with b#95;1 taking the above canonical form must have L#92;ge 3 high-pass filters.

2015 July 27, Bin Han, Qingtang Jiang, Zuowei Shen, Xiaosheng Zhuang, “Symmetric Canonical Quincunx Tight Framelets with High Vanishing Moments and Smoothness [arXiv:1507.07492v1]”, in arXiv:


gonality

If C is reducible, we compare its gonality to that of its irreducible components.

2015, Juliana Coelho, Frederico Sercio, “On the gonality of stable curves”, in arXiv:

(mathematics) The "angularity" of a curve (See the Wikipedia article for a more rigorous definition)


hyperensemble

It is now evident that our hyperensemble has the functional form of the entropic distribution, a probability of probabilities..

2007, Gavin E. Crooks, “Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium”, in Phys. Rev. E, volume 75, →DOI, page 041119:

In particular, we provide a bound on the spectral radius of the symmetric Bernoulli hyperensemble..

2015, Joshua Cooper, “Spectra of Random Hypermatrices and Hypergraphs”, in arXiv:

(mathematics) A group of related probability distributions


minibatch

Attested since 1993, mini- + batch. Quickly displaced original term "blockupdate" coined by Martin Møller in 1992.

Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size.

2015, Elad Hazan, Kfir Y. Levy, Shai Shalev-Shwartz, “Beyond Convexity: Stochastic Quasi-Convex Optimization”, in arXiv:

(machine learning) A batch less than one epoch


multidimensions

Quasi-convexity broadens the concept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient decent.


plurisubharmonic

We prove that any embedded Maslov index two analytic disc attached to a totally real torus in the complex two-dimensional affine space extends to an analytic filling provided that the torus is contained in a regular level set of a strictly plurisubharmonic function..

2015, Kai Zehmisch, “Analytic filling of totally real tori”, in arXiv:

(mathematics) Describing a generalization of subharmonic functions


Steiner tree

(graph theory) The minimum-weight connected subgraph of a graph that includes all the vertices of that graph.


Brocard triangle

en-noun

Brocard triangle (plural Brocard triangles)

Named after Henri Brocard (1845–1922), French mathematician.

(geometry) The triangle formed by joining the points of intersection of the lines from each vertex of a triangle to its Brocard points.


Brocard point

(geometry) The point inside a triangle at the intersection of the lines through each vertex such that the angle between the line and the side of the triangle when moving clockwise is the same for each vertex.


lectic

From Ancient Greek λέγω (légō) + -τικός (-tikós).

(mathematics) Pertaining to a generalization of alphabetical order applied to sets such that, for each pair of sets, their relative ordering is the order obtained if you remove their common (shared) elements and compare the last element in each remaining subset.


milligravity

The unit of the MAD is milligravity (mg); ie, the Earth’s gravity 1g is equal to 1000 mg.

2015 August 21, “Validation of Cut-Points for Evaluating the Intensity of Physical Activity with Accelerometry-Based Mean Amplitude Deviation (MAD)”, in PLOS ONE, →DOI:

A force equal to one thousandth of Earth's gravitational force


mean absolute deviation

mean absolute deviation (plural mean absolute deviations)

(statistics) In a set of data, the average of the absolute values of the deviations from a chosen central point.


codegree

(mathematics) The number of edges of a hypergraph that contain all the specified vertices


eigensheaf

(mathematics) Any sheaf whose value is based on an eigenfunction


eigentriple

(mathematics) Any triple whose values are based on an eigenfunction


quasimodular

(mathematics) Being the holomorphic part of an almost holomorphic modular form.


supercyclic

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

(topology) Having a subspace of hypercyclic vectors


crossbreak

(statistics) A statistical analysis of a data set by two or more variables at once.


Hadamard regularization

Hadamard regularization (usually uncountable, plural Hadamard regularizations)

Introduced by the mathematician Hadamard in 1923.

(mathematics) A method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part.


hypersingular

(mathematics) Of an integral equation: containing Hadamard finite part integrals with f(t) unknown.


overring

(mathematics) An overring B of an integral domain A is a subring of the field of fractions K of A that contains A, i.e. A#92;subseteqB#92;subseteqK.


Weyl group

(mathematics) A subgroup of the isometry group of a root system, generated by reflections through the hyperplanes orthogonal to the roots.


pseudolikelihood

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

(statistics) An approximation to the joint probability distribution of a collection of random variables.


uniformizer

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

uniformizing parameter
uniformizing parameter

(commutative algebra) A uniformizing parameter.


hyperconvex

Furthermore, we deduce a local to global theorem for injective (or hyperconvex) metric spaces, saying that under certain conditions a complete, simply-connected, locally injective metric space is injective.

2015, Benjamin Miesch, “The Cartan-Hadamard Theorem for Metric Spaces with Local Bicombings”, in arXiv:

(mathematics) Of a metric space: injective.


cusp form

(mathematics) A kind of modular form with a zero constant coefficient in the Fourier series expansion.


nonsqueezing

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Relying on Gromov's nonsqueezing theorem for finite dimensional Hamiltonian systems, the argument is to approximate the solutions to the original infinite dimensional Hamiltonian system by a frequency truncated finite dimensional system, and then the nonsqueezing property is transferred to the infinite dimensional system.

2015, Sunghyun Hong, Soonsik Kwon, “Nonsqueezing property of the coupled KdV type system without Miura transform”, in arXiv:

(geometry) Being or relating to the theorem in symplectic geometry stating that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder.


parallelohedron

parallelohedron (plural parallelohedrons or parallelohedra)

parallelohedrons (plural)
parallelohedra (plural)

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(geometry) A polyhedron that can tessellate three-dimensional spaces with face-to-face contacts via translations.


Hilbert curve

First described by the German mathematician David Hilbert in 1891.

(geometry) A continuous fractal space-filling curve.


quotition

(mathematics) An approach to division in which one asks how many parts there are, rather than (as in partition) what the size of each part is.


antigame

The principle is the same as in kicking the provocative boxer or using strategic weapons in response to a tactical nuclear challenge. A strategy designed for refusing to play a game might be called an antigame strategy.

1962, Klaus Eugen Knorr, Limited strategic war:

When capacity to respond to any aggression at a corresponding level of violence does not exist, the strategy of antigame is recommended.

1966, Y. Harkabi, Nuclear War and Nuclear Peace, Transaction Publishers, →ISBN, page 105:

Should either side adopt an uncooperative or "antigame" stance and attempt to destroy its opponent's high command, then the strategy defeats itself and the side that attempted to maintain communications and hold the door open for war termination is disadvantaged.

1988, Stephen J. Cimbala, Rethinking Nuclear Strategy, Scholarly Resources, Incorporated:

(game theory) A strategy in which a player refuses to participate in a game or replaces it with a game with different rules.


lectical

en-adj

lectical (comparative more lectical, superlative most lectical)

more lectical (comparative)
most lectical (superlative)

From lectic + -al, from Ancient Greek λέξις (léxis, “saying, speech; phrase, word”) + Latin -ālis (suffix forming adjectives from nouns or numerals).

der

The lectical order on ^3(A/) is defined by A' < V : <=> 3i : X <,- Y .

1997, Dickson Lukose, Conceptual Structures: Fulfilling Peirce's Dream, →ISBN:

The lectical smallest closed subspace larger than a given subspace S ⊂ A and having weighted density larger than δ is S⊕ ai, where ai is the lexicographically largest attribute which satisfies dense (S⊕ ai)>δ and S ≪i S ⊕ ai.

2008, Tsau Young Lin, Ying Xie, Anita Wasilewska, Data Mining: Foundations and Practice, Springer-Verlag Berlin Heidelberg, page 40

Next we introduce the lectical order on the set of subsets of M.

2013, Hans-Hermann Bock, Wolfgang Polasek, Data Analysis and Information Systems, →ISBN:


lectically

en-adv

lectically (comparative more lectically, superlative most lectically)

more lectically (comparative)
most lectically (superlative)

A subset ACG is called lectically smaller than a subset B # A if the smallest element which distinguishes A and B belongs to B

1999, Bernhard Ganter, Rudolf Wille, Formal Concept Analysis: Mathematical Foundations:

(mathematics) Pertaining to lectic set properties.


coquecigrue

(mathematics) A certain mathematical object in connection with Leibniz algebras.


hyperball

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We find packing densities using congruent hyperballs and determine the smallest density upper bound of non-congruent hyperball packings generated by the above tilings..

2015, Jenő Szirmai, “Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings”, in arXiv:

(geometry) The set of all points that make a hypersphere.


pseudofinite

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(mathematics) Of a field: both quasi-finite (perfect with a unique extension of every positive degree) and pseudo algebraically closed (every absolutely irreducible variety over the field has a point defined over the field).


idoneal

(mathematics) Belonging to the set of positive integers that cannot be expressed as ab + bc + ac for distinct positive integers a, b, and c.


kadam

Cf. Bengali কদম (kodom), corruption of Sanskrit कदम्ब (kadamba).

Kinaram made the elephant sit under a large kadam tree.

2011, Arupa Patangia Kalita, translated by Deepika Phukan, The Story of Felanee, translation of original in Assamese:

Neolamarckia cadamba
Neolamarckia cadamba#Translingual

(India) A tropical evergreen tree, Neolamarckia cadamba (syn. Anthocephalus indicus, Nauclea cadamba), native to South and Southeast Asia.


codirection

en-noun

codirection (countable and uncountable, plural codirections)

It can be shown that the set of hyperbolic codirections consists of distinct pairs of oppositely-directed convex cones.

2003, Krishan L. Duggal, Ramesh Sharma, Recent Advances in Riemannian and Lorentzian Geometries, page 80:

(countable, mathematics) An equation for a hyperplane in the tangent space modulo a factor that is a positive constant; cotangent direction.


pseudospectrum

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(mathematics) A set containing the spectrum of an operator and the numbers that are "almost" eigenvalues.


argmax

We study an optimization strategy that directly uses a maximum a posteriori (MAP) estimate of the argmax of the function.

2015, Zi Wang, Bolei Zhou, Stefanie Jegelka, “Optimization as Estimation with Gaussian Processes in Bandit Settings”, in arXiv:

(mathematics) The argument of the maximum: the set of points of a given argument for which a given function attains its maximum value.


spatulous

en-adj

spatulous (comparative more spatulous, superlative most spatulous)

more spatulous (comparative)
most spatulous (superlative)

LL-Q1860 (eng)-I learned some phrases-spatulous.wav

From spatula + -ous (suffix forming adjectives denoting presence of a quality, usually in abundance).

suffix

[T]he ſhell of teredo is diſtinguiſhed as being tubular, cylindrical, and open at both ends, lower orifice furniſhed with two lozenge-ſhaped valves, and the upper with two ſpatulous opercules.

1819, Abraham Rees, “CONCHOLOGY”, in The Cyclopædia; or, Universal Dictionary of Arts, Sciences, and Literature. [...] In Thirty-nine Volumes, volume IX, London: Printed for Longman, Hurst, Rees, Orme, & Brown, […] [et al.], →OCLC, column 2:

The Nova Scotian Giantess.—A correspondent had the opportunity of inspecting this remarkably large female [Anna Swan] during the exhibition at the Egyptian Hall, and forwards the following notes:— [...] The hand is spatulous; the fingers short and subequal in length.

1869 April, “Anthropological News”, in The Anthropological Review, volume VII, number XXV, London: Asher & Co., […], →OCLC, page 215:

[page 10] Spatulous fingers, by which I mean those somewhat splay shaped, devote themselves to the useful, especially the physically useful, such as agriculture. [...] [page 11] Such fingers have superabundant energy, and though at first sight war appears utterly opposed to the qualities belonging to this spatulous type, it often affords an outlet to a craving for action and excitement which must find vent.

1886, Eveline Michell Farwell, “Square and Spatulous Tips”, in Fingers and Fortune: A Guide-book to Palmistry, 2nd edition, London: David Stott, […], →OCLC, pages 10–11:

And he would turn to Miss Moorsom for approval, lowering protectingly his spatulous nose and looking up with feeling from under his absurd eyebrows, which grew thin, in the manner of canebrakes, out of his spongy skin.

1913 December, Joseph Conrad, “The Planter of Malata”, in Within the Tides: Tales, London, Toronto, Ont.: J[oseph] M[alaby] Dent & Sons Ltd., published 1915, →OCLC, chapter IV, page 44:

Braking mechanism for the front wheels of motor cars comprising a bearing cap mounted on the stub-axle of the car, a double lever pivotally mounted in said bearing cap one end of said lever being of spatulous shape, [...]

1921 July 25, Marius Adenot, Braking Mechanism for the Front Wheels of Motor Cars, US Patent 1,437,080, column 2, lines 59–64:

A group of syringoceles may open into the urethra by a spatulous ostium; these are classified as perforated syringoceles.

2005, W. van’t Hoff, P. G. Duffy, “Urolithiasis”, in David M. Burge, D. Mervyn Griffiths, Henrik A. Steinbrecher, Robert A. Wheeler, editors, Paediatric Surgery, 2nd edition, London: Hodder Arnold; Boca Raton, Fla.: CRC Press, →ISBN, part 6 (Urology), page 481, column 2:

Resembling a spatula in shape; having a round, flat tip.


hyperbolic geometry

en-noun

hyperbolic geometry (countable and uncountable, plural hyperbolic geometries)

The terminology was introduced in 1871 by Felix Klein, who classified some non-Euclidean geometries as hyperbolisch (“hyperbolic”), elliptisch (“elliptical”), and parabolisch (“parabolic”).

parallel postulate
parallel postulate#English

(geometry) A type of geometry that rejects the parallel postulate. Given a straight line L and a point p not on L, more than one straight line can be drawn through p without intersecting L.

(geometry) A non-Euclidean geometry, that features the hyperbola as geodesic, and has constant negative curvature


hyperring

(mathematics) A nonempty set R that supports hyperaddition as an abelian hypergroup with neutral element 0, multiplication as a monoid with identity element one, supports the distributive law, and for which multiplication by zero always yields the result 0.


figure of eight

figure of eight (plural figures of eight)


isthmoid

(graph theory) A set of vertices of a graph after whose deletion the graph is no longer connected.


pretrain

en-verb

pretrain (third-person singular simple present pretrains, present participle pretraining, simple past and past participle pretrained)

pretrains (present singular third-person)
pretraining (participle present)
pretrained (participle past)
pretrained (past)

Our algorithm pretrains a CNN using a large set of videos with tracking ground-truths to obtain a generic target representation.

2015, Hyeonseob Nam, Bohyung Han, “Learning Multi-Domain Convolutional Neural Networks for Visual Tracking”, in arXiv:

(machine learning) To train (a neural network) on some data set (typically a large generic data set, the output of which one is not directly interested in) before fine-tuning the network on another dataset one is interested in.


pretrained

(machine learning, of a model) Trained on a (usually large) dataset by someone else.


GSO

geosynchronous orbit
geosynchronous orbit#English


secret sharing

(cryptography) Any method for distributing a secret amongst a group of participants, each of whom is allocated a share; the secret can be reconstructed only when a sufficient number of shares (possibly of different types) are combined.


Hermite interpolation

(mathematics) A method of interpolating data points as a polynomial function.


Gibbs phenomenon

After J. Willard Gibbs, who identified the behaviour in 1899, unaware of its previous discovery in 1848 by Henry Wilbraham.
A widespread myth has it that the phenomenon was observed in a device developed in 1898 by Albert A. Michelson to compute and synthesise Fourier series, but that it was assumed due to physical imperfections in the device. In fact, the graphs produced were not precise enough for the phenomenon to be clearly observed, and Michelson made no mention of it in a paper describing the device.

The Gibbs phenomenon is characteristic of Fourier series at a discontinuity, its size being proportional to the magnitude of the discontinuity.

1974, K. F. Riley, Mathematical Methods for the Physical Sciences, Cambridge University Press, page 197:

At a point of discontinuity, the oscillations accompanying the Gibbs phenomenon have an overshoot of approximately 18% of the amplitude of the discontinuity.

1999, Werner S. Weiglhofer, Kenneth A. Lindsay, Ordinary Differential Equations and Applications, page 121:

The observed “ringing” is due to the Gibbs phenomenon, which relates to the inability of a finite Fourier spectrum to reproduce sharp edges.

2007, Uwe Meyer-Baese, Digital Signal Processing with Field Programmable Gate Arrays, 3rd edition, Springer, page 173:

(mathematics) A behaviour of the Fourier series approximation at a jump discontinuity of a piecewise continuously differentiable periodic function, such that partial sums exhibit an oscillation peak adjacent the discontinuity that may overshoot the function maximum (or minimum) itself and does not disappear as more terms are calculated, but rather approaches a finite limit.

Albert A. Michelson
Gibbs phenomenon
Henry Wilbraham
J. Willard Gibbs


Runge's phenomenon

Discovered by Carl David Tolmé Runge (1901).

(mathematics) A problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points.


PERMANOVA

analysis of variance
analysis of variance#English

(statistics) Acronym of permutational multivariate analysis of variance.


coequalizer

(category theory) An arrow whose domain is the codomain of a parallel pair of arrows and which forms part of the colimit of that parallel pair.


copower

(category theory) The dual object of a power.


Kan extension

Named after Jewish and Dutch mathematician Daniel M. Kan (1927–2013), who constructed certain (Kan) extensions using limits in 1960.

2010, Matthew Ando, Andrew J. Blumberg, David Gepner, Twists of K-Theory and TMF, Robert S. Doran, Greg Friedman, Jonathan Rosenberg, Superstrings, Geometry, Topology, and C*-algebras, American Mathematical Society, page 34,
Moreover, f∗ admits both a left adjoint f_! and a right adjoint f_∗, given by left and right Kan extension along the map SingY→SingX, respectively. Note that this is left and right Kan extension in the ∞-categorical sense, which amounts to homotopy left and right Kan extension on the level of simplicial categories or model categories.

2012, Rolf Hinze, Kan Extensions for Program Optimisation, Or: Art and Dan Explain an Old Trick, Jeremy Gibbons, Pablo Nogueira (editors), Mathematics of Program Construction: 11th International Conference, MPC 2012, Proceedings, Springer, Lecture Notes in Computer Science: 7342, page 336,
We can specialise Kan extensions to the preorder setting, if we equip a preorder with a monoidal structure: an associative operation that is monotone and that has a neutral element.

We are going to introduce the direct and inverse image functor for presheaves as special Kan extensions and show that they behave well with respect to global and local model structures on simplicial model categories.

2013, Franz Vogler, Derived Manifolds from Functors of Points, Logos Verlag, page 5:

(category theory) A construct that generalizes the notion of extending a function's domain of definition.

extension de Kan

construct that generalizes the extending of a function's domain of definition


leafwise

In particular, in the case where the boundary holonomy is infinitely tangent to the identity, we determine the structure of the group of leafwise holomorphic automorphisms.

2015, Tomohiro Horiuchi, “Reeb components of leafwise complex foliations and their symmetries II”, in arXiv:

(mathematics, computing theory) In terms of the leaves of a tree or similar data structure.


subtour

The resulting problem is solved to integer optimality, violated constraints (which are trivial to find) are added and the process is repeated until a feasible solution is found. In order to speed up the algorithm we pursue several attempts to find as many relevant subtours as possible.

2015, Ulrich Pferschy, Rostislav Stanek, “Generating subtour elimination constraints for the TSP from pure integer solutions”, in arXiv:

(graph theory) A tour that makes up part of a larger tour.


Winchester gallon

en-noun

Winchester gallon (plural Winchester gallons)

(British) a unit of volume equal to two Winchester quarts, equal to four quarts, or around 4.55 litres.


geomathematics

(mathematics) The application of mathematics to the geosciences


fanegada

From Spanish fanegada, from fanega + -ada (“-ful”).

(historical) Synonym of fanega (“traditional Spanish unit of volume, mass, or land area”)


Schur function

(mathematics) A holomorphic function in the Schur class.


Viète's formula

Named after François Viète (1540–1603), who published it in 1593 in his work Variorum de rebus mathematicis responsorum, liber VIII.

(mathematics) An infinite product of nested radicals representing the constant pi: specifically, 2/π=


Vieta's formula

(mathematics) Any of various formulas that relate the coefficients of a polynomial to a sum or product of its roots.


ulp

Abbreviation of unit in the last place or unit of least precision, coined in 1960 by Canadian mathematician and computer scientist William Kahan (born 1933).

The basic concept of two vectors "agreeing to k ulps" (units in the last place) of each entry or of the largest entry allows us to express relationships among computed values and solutions at perturbed data.

1980, Webb Miller, Celia Wrathall, “Software for Roundoff Analysis”, in Software for Roundoff Analysis of Matrix Algorithms, New York, N.Y., London: Academic Press, →ISBN, section 4.2 (Rounding and Perturbations of the Computational Problem), page 86:

Floating point operations are correct to within half an ulp, and the calculation of uvw by two floating point multiplications will be correct within about one ulp (ignoring second-order terms).

1981, Donald E[rvin] Knuth, “Arithmetic”, in The Art of Computer Programming (Addison-Wesley Series in Computer Science and Information Processing), 2nd edition, volume 2 (Seminumerical Algorithms), Reading, Mass.: Addison-Wesley, →ISBN, page 217; 3rd edition, Reading, Mass.: Addison-Wesley, 1997, →ISBN, section 4.2.2 (Accuracy of Floating Point Arithmetic):

The difference between two consecutive machine numbers is called an ulp (unit in the last place, i.e., one digit in the least significant place). The size of an ulp varies depending on where you are in the set of machine numbers. [...] Ideally no function should ever return a result with error exceeding half of an ulp since the distance from the true result to the nearest machine number is always less than half of an ulp, the worst case being when it is exactly halfway between two machine numbers.

1996, “Numerical Mathematics”, in Victor Adamchik et al., edited by Emily Martin, Mathematica 3.0 Standard Add-on Packages, Champaign, Ill.: Wolfram Media; Cambridge, Cambridgeshire: Cambridge University Press, →ISBN, page 369:

If, instead of considering ulps of the "exact" value x, we consider ulps of the floating-point value X, we have a property that is very similar to Property 2, with the interesting difference that it now holds for any value of the radix.

2010, Jean-Michel Muller et al., “Definitions and Basic Notions”, in Handbook of Floating-Point Arithmetic, Boston, Mass., Basel: Birkhäuser, →DOI, →ISBN, section 2.6.1 (The Ulp Function), page 34:

floating-point number
floating-point number

(computer science, mathematics) The value that the least significant digit of a floating-point number represents, used as a measure of accuracy in numeric calculations.


cotorsion

(mathematics) Of an abelian group: whose every extension by a torsion-free group splits.


Scott's trick

(set theory) A method for giving a definition of equivalence classes for equivalence relations on a proper class, relying on the axiom of regularity but not on the axiom of choice.


unitriangular

In this paper we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups G into unitriangular groups UT#95;n(#92;mathbb#123;Z#125;).

2015, Funda Gul, Alexei G. Myasnikov, Mahmood Sohrabi, “Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group”, in arXiv:

(mathematics) Of a matrix: such that the entries on the main diagonal of a (upper or lower) triangular matrix are all 1.


quasi-compact

(topology, of a space) In which has every open cover has a finite subcover.

(mathematics, of a morphism) Having open affine subschemes.


multibump

We construct multibump solutions that connect one integer point to another one in a prescribed way.

2015, Serena Dipierro, Stefania Patrizi, Enrico Valdinoci, “Chaotic orbits for systems of nonlocal equations”, in arXiv:

(mathematics) Having more than one bump (when visualised as a graph, etc.).


pseudolinear

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

(mathematics) Both pseudoconvex and pseudoconcave.


tesseractic

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

(geometry) Relating to a tesseract; relating to four-dimensional space or to a 4-polytope


Feistel cipher

Named after the German-born physicist and cryptographer Horst Feistel.

(cryptography) A symmetric structure used in the construction of block ciphers. It is an iterated cipher with an internal function called a round function.


rhamphoid

Borrowed from Ancient Greek ῥάμφος (rhámphos, “beak”) + -oid.

(mathematics) Of a cusp: defined by the equation (y-x²)²=x⁵, which is parametrized by (t²,t⁴+t⁵); having two branches with concavity in the same direction.


trisector

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

(geometry) A line or curve that trisects something.


spinode

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


tomin

From Spanish tomín, from Andalusian Arabic ثُمْن (ṯúmn), from Arabic ثُمْن (ṯumn, “one-eighth”), from the root ن (n) م (m) ث (ṯ-m-n). Originally used in reference to it forming one-eighth of a castellano.

(historical) A traditional Spanish unit of mass, equivalent to about 0.6 g.

(historical) A former gold Spanish coin, notionally equivalent to a tomin in weight.

(historical) A former silver colonial Spanish coin, notionally equivalent to a gold tomin in value.


subfactorial

(mathematics, combinatorics) The result of deranging a number. In equations, it is usually symbolised by an exclamation mark (!) before the number being deranged (as opposed to factorials, where the exclamation mark occurs after the number).


factorion

From factor + -ion, coined by Clifford A. Pickover.

145 is a factorion because 1! + 4! + 5! = 1 + 24 + 120 = 145.

(mathematics) A number that is equal to the sum of the factorials of its digits.


tetraspace

Out in tetraspace, skysurfing uniquely provides athletes the power to maneuver move up/down left/right and forward/backward, and to control their relative speed, which counts as a fourth dimension if you enjoy science, science fiction or psychotropic mushrooms.

2009, Michael J. Rosen, No Dribbling the Squid: Octopush, Shin Kicking, Elephant Polo, and Other Oddball Sports:

The shape that results from this extension of a cube into tetraspace is called a tesseract, or 4-hypercube (Figure 3.9).

2011, David M. Boje, Storytelling and the Future of Organizations: An Antenarrative Handbook:

I cannonball through tetraspace on my quest to find Mariko.


volume integral

volume integral (plural volume integrals)

(mathematics) An integral over a 3-dimensional domain.


semimatrix

From this semimatrix, mean within-population pairwise values were calculated with 999 permutations, and 1,000 bootstraps in GenAlEx 6.5 [51 ].

2015 September 23, “Population Genetic Patterns of Threatened European Mudminnow ( Umbra krameri Walbaum, 1792) in a Fragmented Landscape: Implications for Conservation Management”, in PLOS ONE, →DOI:


spectral theory

spectral theory (plural spectral theories)

(mathematics) Those theories extending the eigenvalue and eigenvector theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.


Gbps

We measure bandwidth by Gbps.

(computing) gigabits per second, a measure of data transfer rate equal to 1,000 megabits per second.


gamma distribution

gamma distribution (plural gamma distributions)

The gamma distribution is positively skewed and along with the Weibull, lognormal, and inverse Gaussian (IG) distributions is also available as a model in reliability and life-span studies.

1988, A. Clifford Cohen, Betty Jones Whitten, Parameter Estimation in Reliability and Life Span Models, Marcel Dekker, page 93:

1999 [1977, Wiley], Jean Dickinson Gibbons, Ingram Olkin, Milton Sobel, Selecting and Ordering Populations: A New Statistical Methodology, SIAM, Republished unabridged and corrected, page 328,
The ranking and selection problems in this chapter apply to populations that follow the gamma distribution. The gamma distribution model is used widely in many fields of applications, particularly in engineering and the social and physical sciences.

The negative exponential distribution is a special case of the gamma distribution in which k#61;1. Another important special case of a gamma distribution with parameters k and #92;theta#61;2 is the χ² distribution G(k,2) with n#61;2k degrees of freedom.[…]Gamma distributions have an additivity property: the sum of two random variables following gamma distributions G(k#95;1,#92;theta) and G(k#95;2,#92;theta) is a random variable following a gamma distribution G(k#95;1#43;k#95;2,#92;theta) with parameters k#95;1#43;k#95;2 and #92;theta[…].

2005, M. T. Todinov, Reliability and Risk Models: Setting Reliability Requirements, Wiley, page 36:

exponential distribution
exponential distribution

chi-square distribution
chi-square distribution

(probability theory, statistics) Any of a family of two-parameter continuous probability distributions, of which the common exponential distribution and chi-square distribution are special cases.


log-linear

(mathematics) Being or relating to a mathematical model that takes the form of a function whose logarithm is a linear combination of the parameters of the model, making it possible to apply (possibly multivariate) linear regression.


polygenically

(genetics, mathematics) In a polygenic manner.


Kazhdan-Lusztig polynomial

Kazhdan-Lusztig polynomial (plural Kazhdan-Lusztig polynomials)

Introduced by David Kazhdan and George Lusztig in 1979.

(mathematics, representation theory) A member P_(y,w)(q) of a certain family of integral polynomials that are indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group.


starlikeness

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

(geometry) The property of being starlike.


subpolynomial

(mathematics) Growing at a lesser rate than polynomial.


kirat

From Arabic قِيرَاط (qīrāṭ). Doublet of carat.

bor

Arabic قِيرَاط (qīrāṭ)

A Middle Eastern unit of area, ¹⁄₂₄ of a feddan.


Pachner move

(topology) Any of a set of ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homoeomorphic manifold.


Kodaira vanishing theorem

(mathematics) A basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero.


semipositivity

(mathematics) The property of being semipositive.


overdispersive

en-adj

overdispersive (comparative more overdispersive, superlative most overdispersive)

more overdispersive (comparative)
most overdispersive (superlative)

(statistics) Exhibiting or relating to overdispersion.


underdispersive

underdispersive (comparative more underdispersive, superlative most underdispersive)

more underdispersive (comparative)
most underdispersive (superlative)

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

(statistics) Exhibiting or relating to underdispersion.


boomerish

boomerish (comparative more boomerish, superlative most boomerish)

more boomerish (comparative)
most boomerish (superlative)

He identifies a lot with the Buster attitude, but when it comes to management style, he tends to be very performance-oriented, very Boomerish. He fixes his eyes on the goal, and sometimes he's hurt his relationships with people in that process.

1996, Tim Celek, Dieter Zander, Patrick Kampert, Inside the Soul of a New Generation, page 143:

Where “1999” proposed an apathetic solution to the problem of the oncoming apocalypse—dance!—in “America” Prince sees dystopia and offers nothing but what he sees: No solutions, no boomerish optimism, he's just a camera.

2013, Touré, I Would Die 4 U: Why Prince Became an Icon, page 66:

A Howard Beale for the Instagram era, he’s here lashing out on behalf of boomerish power lunchers who believe in a woman’s right to a safe abortion and oppose police brutality but are too scared to admit how enraged they are by a generation of absolutist woke whiners.

2021 July 17, Jacob Bernstein, “Keith McNally Stirs the Pot”, in The New York Times:


equicharacteristic

(mathematics) Of a ring: such that the ring and its residue field have the same characteristic.


triconnected

(graph theory) Of a connected graph: needing three vertices removed for it to become disconnected.


vertex form

en-noun

vertex form (countable and uncountable, plural vertex forms)

Named because of its use in finding the vertex of a parabola: (h,k).

(mathematics, algebra) a quadratic equation in the form y=a(x-h)²+k


domatic

Sleep scheduling is a standard approach for balancing energy consumption, which has been abstracted as the domatic partition problem.

2014, Zhipeng Cai, Chaokun Wang, Siyao Cheng, Wireless Algorithms, Systems, and Applications, →ISBN, page 379:

(mathematics) Pertaining to a partition into disjoint dominating sets.


rhombitrihexagonal

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

(geometry) Relating to a semiregular tiling of the Euclidean plane with one triangle, two squares, and one hexagon on each vertex.


isotoxal

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(geometry, of a polytope or tiling) That has symmetries which act transitively on its edges.

edge-symmetric

having symmetries that act transitively on its edges


acylindrical

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multimagic

(mathematics) Of a magic cube: remaining magic even if all its numbers are replaced by their kth power.


bimagic

(mathematics) Of a magic cube: remaining magic even if all its numbers are replaced by their kth power for 1 ≤ k ≤ 2.


trimagic

(mathematics) Of a magic cube: remaining magic even if all its numbers are replaced by their kth power for 1 ≤ k ≤ 3.


tetramagic

(mathematics) Of a magic cube: remaining magic even if all its numbers are replaced by their kth power for 1 ≤ k ≤ 4.


nontangentially

(mathematics) In a manner that is not tangential.


hexadecile

From hexa- + decile or hexadeca- + -ile.

The assessor can then be asked to successively divide an interval into equally likely segments yielding the octiles (X_(.125), X_(.875)), hexadeciles (X_(.0625), X_(.9375)), etc., etc.

1974, Robert George Gough, Improving the Quality of and Aggregating Opinions Expressed as Subjective Probability Distributions [unpublished Ph.D. dissertation], Stanford, Calif.: Stanford University, →OCLC, page 16:

With each of the above methods, the quartile values are always either one of the data points, or exactly half way between two data points. Those methods involve only simple arithmetic and are easily extendable to octiles (eighths), hexadeciles (sixteenths), etc. They are not, however, extendable to quintiles (fifths) or percentiles (hundredths), etc. Furthermore, they tend to have a high bias. (That is, the quartile values calculated on subsets of the data set tend to vary more, and are not good predictors of the quartile values of the entire data set.)

2002 July 20, “Defining Quartiles”, in Ask Dr. Math, The Math Forum, Goodwin College of Professional Studies, Drexel University, archived from the original on 2015-09-06:

(statistics) Any of the quantiles which divide an ordered sample population into sixteen equally numerous subsets; a subset thus obtained.


hexadecile

Parameters are then non-linearly re-scaled to the range of 0 to 15 to create a 4 bit acoustic vector component. Empirical non-linear scales were pre-determined for each parameter such that, over the long term, their values distributed evenly across a set of hexadecile bins representing the full range of the parameter. In the current system a separate non-linear scaling was established for each individual speaker, and, given the extent of the ANDOSL data used, this amounted to deriving equiprobable bins from approximately 10 minutes of spoken phonemically-rich sentence data.

2001, J. B[ruce] Millar with D[avid] R[ichard] L[lewellyn] Davies, “A Reassessment of Temporal Information in Speech Processing [Workshop on Innovative Speech Processing, Stratford-upon-Avon, England, 2–3 April 2001]”, in Proceedings of the Institute of Acoustics, volume 23, number 3, St. Albans, Hertfordshire: Institute of Acoustics, →ISSN, archived from the original on 2011-03-02, pages 247–258:

Several algorithms were tested for the equi-population transform. The simplest consisted of dividing the total population by 16 and then, in a single linear scan, the parameter histogram was divided into hexadecile units. This approach performed poorly where parameter distributions were peaky, which is often the case.

2002 March, David Richard Llewellyn Davies, Representing Time in Automated Speech Recognition [unpublished Ph.D. dissertation], Canberra, A.C.T.: Australian National University, →OCLC, archived from the original on 2022-11-10, page 66:

(statistics) Of or relating to a hexadecile.


Kurzweil singularity

Kurzweil singularity (plural Kurzweil singularities)

From Kurzweil + singularity, after the futurist Ray Kurzweil, who used the term singularity in his works to describe this event.

artificial intelligence
artificial intelligence

(artificial intelligence) The point, resulting from ever-accelerating technological progress, when a sufficient threshold of self-evolving artificial intelligence is reached to result in a superintelligence beyond human conception.


Nakamoto

Nakamoto consensus

Nakamoto protocol

(cryptocurrencies) Of, or pertaining to, the blockchain technologies promulgated by Satoshi Nakamoto.


scalebound

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From scale + bound, coined by the mathematician Benoit Mandelbrot in a 1981 paper.

(geometry) Of an object: for which characteristic elements of scale, such as length and width, are few in number and each with a clearly distinct size.


backchain

en-verb

backchain (third-person singular simple present backchains, present participle backchaining, simple past and past participle backchained)

backchains (present singular third-person)
backchaining (participle present)
backchained (participle past)
backchained (past)

(computing, artificial intelligence) To perform inferences, starting with a list of goals (or a hypothesis) and working backwards from the consequent to the antecedent.


gammoid

Named by J. H. Mason in a 1972 paper (On a Class of Matroids Arising From Paths in Graphs).

(mathematics) A certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint paths in a directed graph.


FILF

en-noun

FILF (countable and uncountable, plural FILFs)

In this paper, fuzzy integrated logical forecasting (FILF) and extended FILF (E-FILF) algorithms are suggested for short term forecasting purposes,” wrote 0.

2012, Issues in Artificial Intelligence, Robotics and Machine Learning, →ISBN, page 317:

The aim of this paper is to improve the fuzzy logical forecasting model (FILF) by utilizing multivariate inference and the partitioning problem for an exponentially distributed time series by using a multiplicative clustering approach.

2012, Mathematics—Advances in Research and Application, →ISBN:

In this paper, the fuzzy integrated logical forecasting (FILF) method is extended to improve FTS forecasting by considering seasonal effect on data sets and it is called seasonal FILF (SFILF) method.

2013, Emrah Bulut, Shigeru Yoshida, “Seasonal Fuzzy Integrated Logical Forecasting (SFILF) Model for the Time Charter Rates of Dry Bulk Shipping”, in IAME 2013:

(mathematics) Initialism of fuzzy integrated logical forecasting.


thrackle

Scots term for a fouled fishing line, which Conway heard when visiting Scotland.

We prove that a thrackle drawing containing a standard musquash (standard n-gonal thrackle) cannot contain any other cycle of length three or five.

2016, Grace Misereh, Yuri Nikolayevsky, “Thrackles containing a standard musquash”, in arXiv:

(graph theory) An embedding of a graph in the plane, such that each edge is a Jordan arc and every pair of edges meet once.


unirational

(mathematics) Of a variety V over a field K: being dominated by a rational variety, so that its function field K(V) lies in a pure transcendental field of finite type.


sextantal

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biset

(mathematics) A pair of ordered sets of the same magnitude.


Ree group

(mathematics) A group of Lie type over a finite field constructed from an exceptional automorphism of a Dynkin diagram that reverses the direction of the multiple bonds, generalizing the Suzuki group.


Fitting subgroup

Fitting subgroup (plural Fitting subgroups)

(mathematics) For a finite group G: the unique largest normal nilpotent subgroup of G, which intuitively represents the smallest subgroup that "controls" the structure of G when G is solvable.


Tschirnhaus transformation

Tschirnhaus transformation (plural Tschirnhaus transformations)

Developed by Ehrenfried Walther von Tschirnhaus in 1683.

(mathematics) A type of mapping on polynomials that may be defined by means of field theory as the transformation on minimal polynomials implied by a different choice of primitive element.


discriminantal

As applications we discuss connection of these results with properties of Gale transform, the study of the fundamental groups of the complements to discriminantal arrangements and study of the space of generic arrangements of lines in projective plane.

2016, A. Libgober, S. Settepanella, “Strata of discriminantal arrangements”, in arXiv:

(mathematics) Relating to a discriminant.


pseudoline

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(topology) A curve that shares certain topological properties with a line.


semipartial

For each layer thickness, a semipartial correlation (sr) was calculated for explanatory variables including age, gender, axial length, corneal curvature, and signal strength index.

2016 January 28, “Influence of Clinical Factors and Magnification Correction on Normal Thickness Profiles of Macular Retinal Layers Using Optical Coherence Tomography”, in PLOS ONE, →DOI:

(statistics) Being or relating to a form of partial correlation that holds the third variable constant for either X or Y but (unlike a partial correlation) not both.


RSL

(medicine, statistics) Initialism of regional screening level.


quasithin

(mathematics) Of a group: being a finite simple group that resembles a group of Lie type of rank at most 2 over a field of characteristic 2.


hyperlinear

en-adj

hyperlinear (comparative more hyperlinear, superlative most hyperlinear)

more hyperlinear (comparative)
most hyperlinear (superlative)

Indeed, by a profound result of E. Kirchberg, F. Radulescu and N. Ozawa, a group is hyperlinear if and only if it satisfies the Connes embedding conjecture for groups, that is, if and only if its von Neumann algebra embeds into an ultrapower of the hyperfinite II₁ factor R.

2010, Tullio Ceccherini-Silberstein, Michel Coornaert, Cellular Automata and Groups, →ISBN, page 277:

(mathematics, of groups) Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.

We say that a hyperlinear fuzzy function, f say, strictly separates two fuzzy subsets A and B iff the fuzzy hyperplane determined by f and some point x₀ ϵ X strictly separates A and B

1986, Functiones Et Approximatio Commentarii Mathematici:

(mathematics, of a function of hyperreals) Both additive and homogeneous for hyperreal scalars.

We see that hyperlinear convergence doesn't necessarily imply that the series is easy to evaluate for all values of x.

2007, William H. Press, Numerical Recipes 3rd Edition: The Art of Scientific Computing, →ISBN:

(mathematics, of a sequence) Converging very quickly to a limit so that the ratio of adjacent terms tends to zero.

It has been shown in [3] that, at low excitation intensities, the dependence of the emission intensity from a single crystal of AgBr(I) on the excitation intensity is linear while, at high excitation intensities, it becomes hyperlinear.

1981, Doklady: Proceedings of the Academy of Sciences of the USSR:

(mathematics, curve fitting) Increasing exponentially or as a higher polynomial power.


nonsingleton

(mathematics) Not a singleton; containing more than one element.


Bubnoff unit

Named after the geologist Serge von Bubnoff (1888–1957).

A unit of speed (abbreviated B) equal to one meter per 1,000,000 years, used in geology to measure rates of lowering of earth surfaces due to erosion.


semilength

(mathematics) The value of n for a Dyck path that begins at the origin (0,0) and ends at the coordinate (2n,0).


monstrous moonshine

Coined by John Conway and Simon P. Norton in 1979.

(mathematics) The unexpected connection between the Monster group and modular functions, now known to relate to a certain conformal field theory having the Monster group as symmetries.


quasitopological

(mathematics, of a group) Semitopological, and such that the function mapping elements to their inverses is also continuous.


semitopological

(mathematics, of a group G) Having a topology such that, for each c in G, the two functions G → G defined by x↦xc and x↦cx are continuous.


angelicity

(topology) The quality of a Hausdorff space of being angelic.


hom-set

Short for "homomorphism set", because in some categories the morphisms are homomorphisms.

(category theory) The set or collection of all morphisms from A to B for some given ordered pair (A, B) of objects from some given category.


pseudodistance

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

In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data.

2015 October 16, “Robust Portfolio Optimization Using Pseudodistances”, in PLOS ONE, →DOI:

(mathematics) A pseudometric having some characteristics of distance


plabic

Of course, as illustrated in the example above, merely reordering the face variables of a fixed plabic graph by an odd permutation will change the orientation of the resulting volume-form.

2016, Nima Arkani-Hamed, Grassmannian Geometry of Scattering Amplitudes, page 116:


untouchable number

en-noun

untouchable number (plural untouchable numbers)

(mathematics) A positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself).


fraction bar

The fraction bar is a kerned character, so unlike the solidus it will not push the numerals away a full em space.

2006, Gavin Ambrose et al., The Fundamentals of Typography, page 74:

(typography, mathematics) The line separating the numerator from the denominator, whether horizontal, oblique, or diagonal.

breukstreep

line separating numerator from denominator

diagonal mark

as a diagonal line regardless of kerning


monsterology

(mathematics) The study of the Monster group.


Lindelöf

After the Finnish mathematician Ernst Leonard Lindelöf.

(topology, of a topological space) Such that any open cover has a countable subcover.


Holbeinian

en-adj

Holbeinian (comparative more Holbeinian, superlative most Holbeinian)

more Holbeinian (comparative)
most Holbeinian (superlative)

a Holbeinian circuit

(mathematics) Including every edge exactly once and where, for all x and y, the edges (x,y) and (y,x) have opposite parities.


GCM

Galois/Counter Mode
w:Galois/Counter Mode

(cryptography) Initialism of Galois/Counter Mode.


buckyonion

Blend of buckminsterfullerene + onion, modelled on earlier buckyball, with reference to the concentric layers of an onion.

Detections of C60 and C70 fullerenes in planetary nebulae (PNe) of the Magellanic Clouds and of our own Galaxy have raised the idea that other forms of carbon such as hydrogenated fullerenes (fulleranes like C60H36 and C60H18), buckyonions, and carbon nanotubes, may be widespread in the Universe.

2016, J. J. Díaz-Luis, D. A. García-Hernández, A. Manchado, F. Cataldo, “A search for hydrogenated fullerenes in fullerene-containing planetary nebulae”, in arXiv:

(chemistry) A concentric multishell fullerene structure.


apeirogonal

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(geometry) Having the form of an apeirogon.


tetranomial

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RAG

retrieval-augmented generation
w:retrieval-augmented generation

large language model
large language model

(machine learning) Initialism of retrieval-augmented generation: a method of augmenting performance of LLMs (large language models) by serving them a curated selection of data input, via a combination of relevant data libraries and on-the-fly but relevant search results.


Tribonacci

Elite uses a pseudorandom number generator based on Tribonacci numbers. Unlike Fibonacci numbers, where the nth term in the series is based on the previous two terms, Tribonacci numbers use the previous three terms: […]

2016, John Aycock, Retrogame Archeology, Springer, →ISBN, page 113:

(mathematics) A variant of the Fibonacci sequence in which the preceding three terms, rather than the preceding two, are summed at each iteration.


Reidemeister move

en-noun

Reidemeister move (plural Reidemeister moves)

(mathematics, knot theory) Any of three local moves on a link diagram: (i) twist and untwist in either direction; (ii) move one loop completely over another; (iii) move a string completely over or under a crossing.


chunklet

(statistics, computer science) A group of data points belonging to the same constraint cluster.


constraint cluster

constraint cluster (plural constraint clusters)

(statistics, computer science) a cluster of data points in a set conforming to the must-link and cannot-link constraints specified for each pair of data points


must-link

(statistics, computer science) Of data points: having the property that they must be clustered into the same chunklet.


cannot-link

(statistics, computer science) the property of data points that must not be clustered into the same chunklet


pentadecathlon

X! Produces a westward stream of lightweight spaceships representing prime numbers: a LWSS escapes past the pentadecathlon around generation 120n+100 if and only if n is prime.

1993 March 16, David Bell, “Life program (part 6/18)”, in comp.theory.cell-automata (Usenet):

The speed was very dependent on the number of live cells, but it ran the pentadecathlon at 92 gen/sec in the last version I measured.

2002 July 23, Owen Rees, “Wolfram and "general 2D simulators"”, in comp.theory.cell-automata (Usenet):

(cellular automata) A particular oscillator that returns to its initial state after 15 generations.


functor category

functor category (plural functor categories)

natural transformation
natural transformation

(category theory) A category whose objects are functors (from some fixed given domain category to some fixed given codomain category) and whose morphisms are natural transformations.


natural isomorphism

natural isomorphism (plural natural isomorphisms)

(category theory) A natural transformation whose every component is an isomorphism.


identity morphism

identity morphism (plural identity morphisms)

(category theory) A unique morphism corresponding to each object of a category, which has its domain equal to its codomain, and which composed with any morphism (with which it is composable) gives that same morphism.


identity functor

identity functor (plural identity functors)

(category theory) A functor from a category to itself which maps each object of that category to itself and each morphism of that category to itself.


impulse response

impulse response (plural impulse responses)

(signal processing) Output of a dynamic system when presented with a brief input signal.


Hindu-Arabic numeral

Hindu-Arabic numeral (plural Hindu-Arabic numerals)


comma category

comma category (plural comma categories)

Given a pair of functors S:𝒜→𝒞 and T:ℬ→𝒞, objects of the comma category S↓T are arrows h:S(A)→T(B) parametrized by triples (A, B, h), and given morphisms f:A→A' and g:B→B', then a morphism of the said comma category is a commuting square parametrized by the pair (f, g) and spanning the area from h to h':S(A')→T(B') and from S(f) to T(g).

(category theory) A category built out of a pair of functors that have the same codomain.


universal morphism

universal morphism (plural universal morphisms)

(category theory) The terminal object of a comma category from a functor to a fixed object; or, dually, the initial object of a comma category from a fixed object to a functor.


coslice category

coslice category (plural coslice categories)

(category theory) The category opposite to that of a slice category.


flowsnake

From flow + snake, describing its movements, and as a spoonerism for snowflake.


Gosper curve

(computer graphics) A particular fractal object, a space-filling curve that can tile the plane.


adjoint functor

adjoint functor (plural adjoint functors)

(category theory) One of a pair of functors such that the domain and codomain of one of them are identical to the codomain and domain of the other one, respectively, and such that there is a pair of natural transformations which turns the pair of functors into an adjunction.


Grothendieck universe

Grothendieck universe (plural Grothendieck universes)

Named after Alexander Grothendieck (1928–2014), a German-born French mathematician.

(mathematics, category theory) A kind of universal set whose elements follow the rules of Zermelo–Fraenkel set theory, and for which, with respect to an arbitrary set, an instance of its kind which has that set as a member may be posited to exist through an additional Tarski–Grothendieck axiom (which is not part of ZF but augments it, yielding Tarski–Grothendieck set theory).


cubic decimetre

cubic decimetre (plural cubic decimetres)

A unit of volume equal to that of a cube having sides each one decimetre in length, equal to 10⁻³ cubic metres and 1 litre. Commonly used in fluid measure and for engine sizes.


cubic decimeter

cubic decimeter (plural cubic decimeters)


V-shaped

Shaped like the letter V; especially, designating one of the two major types of valley (the other being U-shaped), typically formed by flowing water.

A-shaped - B-shaped - C-shaped - D-shaped - E-shaped - F-shaped - G-shaped - H-shaped - I-shaped - J-shaped - K-shaped - L-shaped - M-shaped - N-shaped - O-shaped - P-shaped - Q-shaped - R-shaped - S-shaped - T-shaped - U-shaped - V-shaped - W-shaped - X-shaped - Y-shaped - Z-shaped


strict ordering

strict ordering (plural strict orderings)

(mathematics) A relation which is asymmetric and transitive.


sequent calculus

sequent calculus (plural sequent calculi)

(mathematics, logic) A set of inference rules for deriving true sequents from other true sequents.


subobject classifier

subobject classifier (plural subobject classifiers)

classifying morphism
classifying morphism

(category theory) An object which serves as the codomain of a classifying morphism, together with a "true" global element of the said object.


kernel pair

(category theory) A couple of morphisms which constitute the pullback of a given morphism along itself.


classifying morphism

classifying morphism (plural classifying morphisms)

subobject classifier
subobject classifier

(category theory) A morphism from an object to the subobject classifier which corresponds to a unique subobject of the said object, which subobject is the pullback, along this morphism, of the "true" global element of the subobject classifier.


global element

(category theory) A morphism from the terminal object to a given object (to which it is said to belong).


bibundle

(mathematics) A generalized bundle in a Lie group


bidisc

(mathematics) A polydisc of the second order


circumscribed circle

circumscribed circle (plural circumscribed circles)


inscribed circle

inscribed circle (plural inscribed circles)


point of tangency

point of tangency (plural points of tangency)

(geometry) The point where a tangent line and its curve meet

切點 /切点

the point where a tangent line and its curve meet


hyperdegree

(mathematics) The property of a number shared with another number with which it is hyperarithmetical.


hyperoval

(mathematics) A particular set of points, related to an oval, in a projected plane


Cartesian natural transformation

Cartesian natural transformation (plural Cartesian natural transformations)

Cartesian natural transformations (plural)

So called because its naturality squares are Cartesian squares.

(category theory) A natural transformation whose naturality squares are pullbacks.


twist morphism

(category theory) An isomorphism between a pair of products which have the same components but in swapped order, which isomorphism commutes with the two associated product diagrams.


multimapping

(mathematics) A multiple (n to n) mapping


nilsequence

(mathematics) A sequence of zero elements


full binary tree

full binary tree (plural full binary trees)

(mathematics, computing) A binary tree in which each node has exactly two or zero children.


Galton's problem

(statistics) The difficulty in drawing inferences from cross-cultural data, due to the statistical phenomenon of autocorrelation.


raw data

Coined in the 1910s, from raw (“unprocessed”) + data.

Do their speakers semantically align supposedly raw data with supposedly raw text (that is, ASCII) and supposedly raw footage (unedited film or video) the way that English speakers do?

2013, Lisa Gitelman, editor, Raw Data Is an Oxymoron, MIT Press, →ISBN, page 11:

(data management, statistics) Data that has not been analyzed or processed.


Liouville number

Liouville number (plural Liouville numbers)

Named after Joseph Liouville (1809–1882), a French mathematician.

(number theory) An irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that 0<|x-p/q|<1/(qⁿ).


Coxeter group

Named for British-born Canadian mathematician H. S. M. Coxeter (1907–2003).

We may ask in general which Coxeter groups arise as subgroups of a given Coxeter group. This question is of course far too general. However, there are Coxeter groups which arise canonically as subgroups of a given Coxeter group.

1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. de Clerck, editors, Finite Geometries and Combinatorics, page 277:

The above definitions, of Cayley graph, reflection, wall, half-space, folding, Bruhat order, etc., work for any Coxeter group.

2007, Michael B. Smythe, Julian Webster, “12: Discrete Spatial Models”, in Marco Aiello, Ian Pratt-Hartmann, Johan van Benthem, editors, Handbook of Spatial Logics, page 795:

The problem of classifying all reflective lattices of given rank is also of interest in its own right from the perspectives of Coxeter groups and arithmetic subgroups of O(n,1).

2012, Daniel Allcock, “The Reflective Lorentzian Lattices of Rank 3”, in Memoirs of the American Mathematical Society, number 1033, page vii:

(mathematics, geometry, group theory) Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.

Coxeter group
Harold Scott MacDonald Coxeter


vertex figure

1970, Harold Scott Macdonald Coxeter, Twisted Honeycombs, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics: Number 4, American Mathematical Society, page 14,
Thus the vertex figure of a polygon is the line-segment whose end-points are the vertex figures of the two edges at one vertex, the vertex figure of a polyhedron or tessellation {p, q} is the polygon {q} whose edges are the vertex figures of the q faces at one vertex, and the analogous "vertex figure" of the honeycomb of cubes (§1) is the polyhedron whose faces are the vertex figures of the eight cubic cells that come together at one vertex.

Now try to see which of these vertex figures cannot be continued to give a semiregular tiling of the whole plane.

1987, A. Gardiner, Mathematical Puzzling, Dover, published 1999, page 137:

At each vertex of a tessellation, the vertex figure is the polygon formed by joining in order the mid-points of all edges incident with the vertex. A tessellation of a surface for which all the participating polygons and vertex figures are regular and equal is termed a regular tessellation.

2004, Michael F. Worboys, Matt Duckham, GIS: A Computing Perspective, 2nd edition, page 188:

(geometry) The figure exposed when a corner of a polyhedron or polytope is sliced off.


birthday effect

(statistics) A statistical phenomenon where an individual's likelihood of death appears to increase on or close to their birthday, variously attributed to alcohol consumption, psychological stress, increased suicide risk, and other factors.


Microsoft minute

Microsoft minute (plural Microsoft minutes)

A derogatory reference to the slow performance of Microsoft software.

(humorous, rare) A unit of time longer than one minute.


Krein-Milman theorem

A less general version was originally proved by Mark Krein and David Milman.

(mathematics, functional analysis) A proposition about convex sets in topological vector spaces.


biweight

We began by mapping peptides to all possible proteins, and we then took the weighted mean (also known as Tukey’s biweight; implemented in the R Bioconductor package “affy”) to obtain a protein intensity that is more robust than the summation of intensities [36 –38 ].

2015 November 6, “A Pilot Proteogenomic Study with Data Integration Identifies MCT1 and GLUT1 as Prognostic Markers in Lung Adenocarcinoma”, in PLOS ONE, →DOI:

(mathematics) Any of various weighted means


jurimetrics

(mathematics, law) The application of quantitative and statistical methods to law.


biadjacency

The matrix can be thought as the biadjacency matrix of the bipartite network [21 –23 ] in which one layer is represented by countries and the other by exported products.

2015 November 7, “From Innovation to Diversification: A Simple Competitive Model”, in PLOS ONE, →DOI:

(mathematics) The adjacency of a bipartite graph


AI winter

By analogy to the idea of a nuclear winter.

A lot of people are talking about — actually have been talking about — a particular scenario of the artificial intelligence industry known as the "AI Winter."

Their products offered little business value at the time, and so the commercial enthusiasm ended in disappointment, leading to a period now referred to as the “A.I. Winter.”

2016 July 17, John Markoff, “Artificial Intelligence Swarms Silicon Valley on Wings and Wheels”, in The New York Times, →ISSN:

(artificial intelligence, economics) A period of reduced funding and interest in artificial intelligence research.


diagonal morphism

diagonal morphism (plural diagonal morphisms)

(category theory) A morphism from an object to the product of that object with itself, which morphism is induced by a pair of identity morphisms of the said object.


subconstituent

The second subconstituent of a graph with respect to some vertex x is the induced graph on the vertices distinct from x, and that are not adjacent to x.

1999, Journal of algebraic combinatorics - Volume 10, page 79:

During 1992 and 1993 Paul Terwilliger introduced a new tool called the subconstituent algebra for studying the underlying structure of association schemes through a series of three papers [21], [22], and [23]. Terwilliger introduced a method for studying commutative association schemes by defining a new algebra that is noncommutative, finite dimensional, semisimple C-algebra. The subconstituent algebra is now popularly referred to as the "Terwilliger" algebra.

2008, Terwilliger Algebras of Wreath Products of Association Schemes, →ISBN:

(mathematics) One component of an algebra or graph that is made up of the union of several subalgebras or subgraphs.


septisect

en-verb

septisect (third-person singular simple present septisects, present participle septisecting, simple past and past participle septisected)

septisects (present singular third-person)
septisecting (participle present)
septisected (participle past)
septisected (past)

(transitive, mathematics, nonce word) to divide a quantity, angle etc into seven equal parts


quinquesect

quinquesect (third-person singular simple present quinquesects, present participle quinquesecting, simple past and past participle quinquesected)

quinquesects (present singular third-person)
quinquesecting (participle present)
quinquesected (participle past)
quinquesected (past)

(transitive, mathematics) To divide (a quantity, angle etc.) into five equal parts.


quinquesection

en-noun

quinquesection (countable and uncountable, plural quinquesections)

(mathematics) Division into five equal parts.


biclosed

(mathematics) Of a monoidal category: both left-closed and right-closed.


cryptovirology

(cryptography, computer security) The use of cryptography to design powerful malicious software such as ransomware and asymmetric backdoors.


eensy-weensy

en-adj

eensy-weensy (comparative more eensy-weensy, superlative most eensy-weensy)

more eensy-weensy (comparative)
most eensy-weensy (superlative)

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oloid

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Furthermore, we derive the expectations of the mean width, the surface area and the volume of the intersections of a fixed oloid and a moving ball, as well as of a fixed and a moving oloid.

2016, Uwe Bäsel, “The mean width of the oloid and integral geometric applications of it”, in arXiv:

(geometry) A three-dimensional curved geometric object, the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the other circle.


Gauss-Seidel method

Named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel.

(mathematics) An iterative method used to solve a linear system of equations.


coclass

(mathematics) The coclass of a finite p-group of order pⁿ is n - c, where c is the class.


laceable

(graph theory) Of a bipartite graph: having a possible Hamiltonian path between any two vertices from different partite sets.


laceability

(graph theory) The property of being laceable.


comeager

(set theory) Alternative form of comeagre


comeagre

(set theory) Being the complement of a meagre set.


softplus

(mathematics) A smooth approximation to the rectifier in neural networks; it is the analytic function f(x)= ln (1+eˣ).


quasicircle

We then use a limiting Cauchy integral along level curves of Green's function to show that the Plemelj-Sokhotski jump formula holds on quasicircles with boundary data in the Douglas-Osborn space, which also enable us to prove the well-posedness of a Riemann-Hilbert problem with boundary data in Douglas-Osborn space on quasicircles.

2016, Eric Schippers, Wolfgang Staubach, “Harmonic reflection in quasicircles and well-posedness of a Riemann-Hilbert problem on quasidisks”, in arXiv:

(mathematics) A Jordan curve in the complex plane that is the image of a circle under a quasiconformal mapping of the plane onto itself.


quasidisk

We show that quasidisks are precisely those Jordan curves for which this reflection is defined and bounded.

(mathematics) The interior of a quasicircle.


OLS

ordinary least squares
ordinary least squares#English

(statistics) Abbreviation of ordinary least squares.


spirallikeness

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(geometry) The property of being spirallike.


LOD

en-noun

LOD (countable and uncountable, plural LODs)

In practice, the LOD score is computed over a wide range of values for 6.

1998, Thomas D. Gelehrter, Francis S. Collins, David Ginsburg, Principles of Medical Genetics, →ISBN, page 200:

For historical reasons, the LOD score functions LOD(Θ) = log ʌ(Θ) is preferred in genetic epidemiologial applications over LR(Θ) = 2ln ʌ(Θ).

2010, Andreas Ziegler, Inke R. König, A Statistical Approach to Genetic Epidemiology, →ISBN, page 158:

One would expect that LOD (logarithm of odds) scores based on small sample sizes would be unstable and contribute to lack of replication.

2005, Linda A. Ferrera, Body Mass Index: New Research, →ISBN, page 150:

(statistics) Alternative letter-case form of lod (“logarithm of odds”)


Galois field

Named after French mathematician Évariste Galois (1811–1832).

named-after

The Galois field #92;mathrm#123;GF#125;(pⁿ) has order pⁿ and characteristic p.

The Galois field #92;mathrm#123;GF#125;(pⁿ) is a finite extension of the Galois field #92;mathrm#123;GF#125;(p) and the degree of the extension is n.

The multiplicative subgroup of a Galois field is cyclic.

A Galois field #92;mathbb#123;F#125;#95;#123;pⁿ#125; is isomorphic to the quotient of the polynomial ring #92;mathbb#123;F#125;#95;p adjoin x over the ideal generated by a monic irreducible polynomial of degree n. Such an ideal is maximal and since a polynomial ring is commutative then the quotient ring must be a field. In symbols: #92;mathbb#123;F#125;#95;#123;pⁿ#125;#92;cong#123;#92;mathbb#123;F#125;#95;p#91;x#93;#92;over(#92;hatf#95;n(x))#125;.

1958 [Chelsea Publishing Company], Hans J. Zassenhaus, The Theory of Groups, 2013, Dover, unnumbered page,
A field with a finite number of elements is called a Galois field.
The number of elements of the prime field k contained in a Galois field K is finite, and is therefore a natural prime p.

The case of most interest to us will be that in which F is a finite field, the Galois field GF(q) for some prime power q. If q is prime, this field is #92;mathbb#123;Z#125;#95;q, the integers 0,1,#92;dots,q-1 with arithmetic modulo q.

2001, Joseph E. Bonin, A Brief Introduction To Matroid Theory, retrieved 2016-05-05:

2006, Debojyoti Battacharya, Debdeep Mukhopadhyay, D. RoyChowdhury, A Cellular Automata Based Approach for Generation of Large Primitive Polynomial and Its Application to RS-Coded MPSK Modulation, Samira El Yacoubi, Bastien Chopard, Stefania Bandini (editors), Cellular Automata: 7th International Conference, Proceedings, Springer, LNCS 4173, page 204,
Generation of large primitive polynomial over a Galois field has been a topic of intense research over the years. The problem of finding a primitive polynomial over a Galois field of a large degree is computationaly expensive and there is no deterministic algorithm for the same.

(algebra) A finite field; a field that contains a finite number of elements.


interedge

(mathematics) An edge whose two nodes are in different networks


Nyquist rate

(signal processing) Twice the bandwidth of a bandlimited function or a bandlimited channel.