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Family of higher-order functions
In functional programming, a fold is a higher-order function that analyzes a recursive data structure and, through use of a given combining operation
Fold_(higher-order_function)
Computer programming function
In many programming languages, map is a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning
Map_(higher-order_function)
Function that takes one or more functions as an input or that outputs a function
computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a
Higher-order_function
Computer programming function
functional programming, filter is a higher-order function that processes a data structure (usually a list) in some order to produce a new data structure containing
Filter (higher-order function)
Filter_(higher-order_function)
Homomorphism from an initial algebra into another algebra
3.000.000. The cata map is closely related to the right fold (see Fold (higher-order function)) of lists foldrList. The morphism lift defined by lift
Catamorphism
Type of function in database management
load Fold (higher-order function) Group by (SQL), SQL clause OLAP cube Online analytical processing Pivot table Relational algebra Utility functions on
Aggregate_function
Topics referred to by the same term
fold, an area of skin that folds Code folding, a techique used by full screen and GUI editors Fold (higher-order function), a type of programming operation
Folding
Table that summarizes data from another table
mining Data visualization Data warehouse Extract, transform, load Fold (higher-order function) OLAP cube Relational algebra Wide and narrow data "United States
Pivot_table
Function definition that is not bound to an identifier
passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a function. If the function is only
Anonymous_function
Microsoft .NET Framework component
finalization function, taking the aggregation result to yet another value, can be supplied. This implements the Fold higher-order function. The Join operator
Language_Integrated_Query
Computer science concept
reductions to be able to handle very big data sets. Fold (higher-order function) Scan (higher-order function) "Reduction Clause". www.dartmouth.edu. Dartmouth
Reduction_operator
Change of a linear protein chain to a 3D structure
essential to function, although some parts of functional proteins may remain unfolded, indicating that protein dynamics are important. Failure to fold into a
Protein_folding
Operation on mathematical functions
square root Functional equation Higher-order function Infinite compositions of analytic functions Iterated function Lambda calculus The strict sense
Function_composition
Representation of natural numbers and other data types in lambda calculus
encoding. The higher-order function that represents natural number n is a function that maps any function f {\displaystyle f} to its n-fold composition
Church_encoding
Programming language feature
mid-1960s. First-class functions are a necessity for the functional programming style, in which the use of higher-order functions is a standard practice
First-class_function
Alternate way to define a function in APL
A direct function (dfn, pronounced "dee fun") is an alternative way to define a function and operator (a higher-order function) in the programming language
Direct_function
respectively. These are functions that operate on functions or produce other functions; see Higher order function. Examples are: Function composition. Integral
List_of_types_of_functions
Area of mathematics
catastrophe has fine diffraction details described by the Pearcey function. Higher-order catastrophes, such as the swallowtail and the butterfly, have also
Catastrophe_theory
Joining of strings in a programming language
Wikifunctions has a concat function. In formal language theory and computer programming, concatenation is the operation of joining sequential objects,
Concatenation
in the folded protein divided by the total length of the protein. Higher contact orders indicate longer folding times, and low contact order has been
Contact_order
passed to higher-order functions or used for constructing the result of a higher-order function that needs to return a function. If the function is only
Examples of anonymous functions
Examples_of_anonymous_functions
Programming function applied recursively to its previous result
(\a->(a,f a)) (\x->False) In a language like Haskell, even the abstract functions fold, unfold and ana are merely defined terms, as we have seen from the definitions
Anamorphism
Special mathematical function
positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams. The polylogarithm function is equivalent to
Polylogarithm
Arrangement of hereditary material
pattern, which encodes information as a function of their order. Genomic organization refers to the linear order of DNA elements and their division into
Genomic_organization
flattened without damaging it), and the use of paper folds to solve mathematical equations up to the third order. Computational origami is a recent branch of
Mathematics_of_paper_folding
Programming paradigm based on applying and composing functions
pattern simply dictates use of a higher-order function, and the visitor pattern roughly corresponds to a catamorphism, or fold. Similarly, the idea of immutable
Functional_programming
Operation in algebraic topology
algebraic topology, the Massey product is a cohomology operation of higher order introduced in (Massey 1958), which generalizes the cup product. The Massey
Massey_product
Sequence in computer science
addition operation); the higher order function resulting from this generalization is called a scan, and it is closely related to the fold operation. Both the
Prefix_sum
Topics referred to by the same term
Unfoldable cardinal, in mathematics Unfold (higher-order function), in computer science a family of anamorphism functions Unfoldment (disambiguation), in spirituality
Unfold
Fundamental trigonometric functions
{d}{dx}}\cos(x)=-\sin(x).} Continuing the process in higher-order derivative results in the repeated same functions; the fourth derivative of a sine is the sine
Sine_and_cosine
Theorem about admissible crystal symmetries
dimensions, the rotational symmetries are restricted to 2-fold, 3-fold, 4-fold, and 6-fold. The theorem's name comes from geological crystals, whose rotational
Crystallographic restriction theorem
Crystallographic_restriction_theorem
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Functions in mathematics
Considering higher dimensional analogues of the harmonics on the unit n-sphere, one arrives at the spherical harmonics. These functions satisfy Laplace's
Harmonic_function
Biomolecule consisting of chains of amino acid residues
alters the physical and chemical properties, folding, stability, activity, and ultimately, the function of the proteins. Some proteins have non-peptide
Protein
Thin fold of skin that covers and protects the eye
An eyelid (/ˈaɪ.lɪd/ EYE-lid) is a thin fold of skin that covers and protects the eye. The levator palpebrae superioris muscle retracts the eyelid, exposing
Eyelid
Measure of similarity between two protein structures
whereas structures with a score higher than 0.5 assume roughly the same fold. A quantitative study shows that proteins of TM-score = 0.5 have a posterior
Template_modeling_score
Function defined by a hypergeometric series
Riemann (1857) of the hypergeometric function by means of the differential equation it satisfies. Riemann showed that the second-order differential equation for
Hypergeometric_function
Additional mathematical object
preserve algebraic structures; continuous functions, which preserve topological structures; and differentiable functions, which preserve differential structures
Mathematical_structure
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Programming language
(succ) and addition (add). A Church numeral n is a higher-order function that accepts a function f and a value x and applies f to x exactly n times.
OCaml
Proof assistant
constructors Implicit arguments for functions applied to zero arguments, which is useful when programming with higher-order functions Concise anonymous arguments
Rocq
around the histone core proteins. Higher-order packaging is accomplished by specialized proteins that bind and fold the DNA. This generates a series of
Eukaryotic chromosome structure
Eukaryotic_chromosome_structure
Self-stabilizing region of a protein that binds to specific DNA sequences
their folded structure. One or more DNA-binding domains are often part of a larger protein consisting of further protein domains with differing function. The
DNA-binding_domain
ETL tool developed by Microsoft
might fold. Non-folding queries will have to be performed on the client-side. The order of queries can determine how many of the steps which get folded. A
Power_Query
Distributed computing project simulating protein folding
the timescales that they can study. While most proteins typically fold on the order of milliseconds, before 2010, simulations could only reach nanosecond
Folding@home
Automatic double-sided printing
Duplex printing is a feature of some computer printers and multi-function printers (MFPs) that allows the printing of a sheet of paper on both sides automatically
Duplex_printing
Comparison of programming languages
future revisions" of the standard.) Similarly, implicit function declarations (using functions that have not been declared) are not allowed in C++, and
Compatibility_of_C_and_C++
Measure of algorithmic complexity
lexicographic order, until one of them outputs the string. The other direction is much more involved. It shows that given a Kolmogorov complexity function, we can
Kolmogorov_complexity
Formal power series
or weighted sums over the higher-order derivatives of these functions (see derivative transformations). Generating function transformations can come into
Generating_function
Loss of structure in proteins and nucleic acids due to external stress
therefore, cannot function. Proper protein folding is key to whether a globular or membrane protein can do its job correctly; it must be folded into the native
Denaturation_(biochemistry)
Mathematical set formed from two given sets
can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be represented by an n-dimensional array, where
Cartesian_product
Ordered chemical structure with no repeating pattern
six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold. Aperiodic
Quasicrystal
Hash function that is suitable for use in cryptography
given only its digest. In particular, a hash function should behave as much as possible like a random function (often called a random oracle in proofs of
Cryptographic_hash_function
Diagram that shows all possible logical relations between a collection of sets
but there are forms that allow for higher numbers. Shown below, four intersecting spheres form the highest order Venn diagram that has the symmetry of
Venn_diagram
Mammalian structure involved in higher-order brain functions
a set of layers of the mammalian cerebral cortex involved in higher-order brain functions such as sensory perception, cognition, generation of motor commands
Neocortex
Predicting 3D protein structure from its sequence
threading strategies, the fold recognition technique is expanded further. In this process, empirically based energy functions for the interaction of residue
De novo protein structure prediction
De_novo_protein_structure_prediction
2-fold proper rotation axes normal to a principal rotation axis. The dihedral groups are denoted by Dn. These groups are characterized by i) an n-fold proper
List of character tables for chemically important 3D point groups
List_of_character_tables_for_chemically_important_3D_point_groups
Multiparadigm programming language
{Square N} % A general function N*N end fun {Map F Xs} % F is a function here - higher order programming case Xs of nil then nil [] X|Xr then {F X}|{Map F
Oz_(programming_language)
Symbols requiring interpretation
may change depending on the model. In first-order logic, these usually consist of constant symbols, function symbols, and predicates. This is in contrast
Non-logical_symbol
School of thought in philosophy of mathematics
to order (1 and 2). By "predicative", Russell meant that the function must be of an order higher than the "type" of its variable(s). Thus a function (of
Logicism
Solutions of Lamé's equation
In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation. It
Lamé_function
association lists, maintain the order of entry insertion. Common Lisp hash tables are constructed via the make-hash-table function, whose arguments encompass
Comparison of programming languages (associative array)
Comparison_of_programming_languages_(associative_array)
Numerical calculations carrying along derivatives
arithmetic can be generalized to calculate second order and higher derivatives of multivariate functions. However, the arithmetic rules quickly grow complicated:
Automatic_differentiation
Programming language
identifiers must be unique in every block. function f(x: integer): real; begin result := sin(x); end; function f(x: real): real; begin result := cos(x);
Comparison of Pascal and Delphi
Comparison_of_Pascal_and_Delphi
Special function called to create an object
object-oriented programming, a constructor (abbreviation: ctor) is a special type of function called to create an object. It prepares the new object for use, often accepting
Constructor (object-oriented programming)
Constructor_(object-oriented_programming)
Calculus of vector-valued functions
k-vector field can be identified with a scalar function or vector field, but this is not true in higher dimensions). This replaces the cross product, which
Vector_calculus
Calculus for deriving computer programs
using the Larch Prover. Map is a well-known second-order function that applies a given function to every element of a list; in BMF, it is written ∗ {\displaystyle
Bird–Meertens_formalism
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Theory in the domain of evolutionary biology
is 4 times higher than for P1: this bias can be mapped to the Yampolsky-Stoltzfus model and would have the same implications as a 4-fold mutation bias
Bias in the introduction of variation
Bias_in_the_introduction_of_variation
Description of non-logical symbols
n} -fold cartesian product of the domain A {\displaystyle A} with itself, and so f {\displaystyle f} is in fact an n {\displaystyle n} -ary function, and
Signature_(logic)
Characteristic of an optical system
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector is a scale-dependent description of their
Optical_transfer_function
Topics referred to by the same term
(Berkeley Internet Name Daemon), Domain Name System software Bind (higher-order function), an operation in a monad Bind, a client to a server in client–server
Bind
complexes. MacLean proposes that the neomammalian complex is only found in higher order mammals, for example, the human brain, accounting for increased cognitive
Neomammalian_brain
Two-dimensional state of matter
translational order can be determined with the translational correlation function G G → ( R → ) {\displaystyle G_{\vec {G}}({\vec {R}})} as function of the distance
Hexatic_phase
Rational design of new protein molecules
determined by the protein design energy function. Thus, a typical input to the protein design algorithm is the target fold, the sequence space, the structural
Protein_design
Spectral line splitting in electrical field
2(2J+1)-fold degenerate energy for |K| > 0 and (2J+1)-fold degenerate energy for K=0. Here DJMK is an element of the Wigner D-matrix. The first-order perturbation
Stark_effect
Programming language family
structures, automatic storage management, dynamic typing, conditionals, higher-order functions, recursion, the self-hosting compiler, and the read–eval–print loop
Lisp_(programming_language)
How many times a number is divisible by 2
children's teaching materials including higher multiples such as "quadruply even." One can also extend the 2-order to the rational numbers by defining ν2(q)
Singly_and_doubly_even
DNA mutation with no observable effect on an organism's phenotype
efficiency and protein folding and function. Furthermore, a change in primary structure is critical because the fully folded tertiary structure of a
Silent_mutation
Axiomatic set theories based on the principles of mathematical constructivism
the use of some total functions. A similar distinction is not relevant on the level Σ 1 0 {\displaystyle \Sigma _{1}^{0}} or higher. Finally note that a
Constructive_set_theory
Oscillating dynamical system with nonlinear damping
geological fault, and in studies of phonation to model the right and left vocal fold oscillators. Liénard's theorem can be used to prove that the system has a
Van_der_Pol_oscillator
Camera feature of combining shots
in the field. The Minolta Maxxum 7's STF function is an automatically calculated and pre-compensated seven-fold multi-exposure with depth-of-field bracketing
Autobracketing
Biomolecular structure of nucleic acids such as DNA and RNA
It is a higher order than the secondary structure, in which large-scale folding in a linear polymer occurs and the entire chain is folded into a specific
Nucleic_acid_structure
Number of available physical states per energy unit
mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the
Density_of_states
Method for measuring urban sprawl
Montreal, the degree of urban sprawl increased 26-fold, Quebec City increased 9-fold, and Zurich 3-fold. Torres, Jaeger & Alonso (2016) quantified spatial
Weighted_urban_proliferation
Protein in Streptomyces avidinii
named traptavidin, was found to have more than ten-fold slower biotin dissociation, in addition to higher thermal and mechanical stability. This decreased
Streptavidin
Branch of mathematical analysis
Mittag-Leffler function has a particular case E 1 {\displaystyle E_{1}} , which is the exponential function, the Mittag-Leffler distribution of order 1 {\displaystyle
Fractional_calculus
telomere length. In fungus, the CST complex has been shown to unfold higher order G-tailed structures, such as occur with telomere exposure during DNA
CST_complex
Mammalian protein found in humans
inhibitors, PMs exhibit a drug exposure that is 3 to 13 times higher than that of EMs. Loss-of-function alleles, CYP2C19*2 and CYP2C19*3 (and others, which are
CYP2C19
Geometric symmetry in living beings
equilateral triangle, and 12 corners. Within the icosahedron there is 2-fold, 3-fold and 5-fold symmetry. Many viruses, including canine parvovirus, show this
Symmetry_in_biology
Technique for selecting hash functions
To obtain a truly 'universal' hash function, one can use the multiply-add-shift scheme that picks higher-order bits h a , b ( x ) = ( ( a x + b ) mod
Universal_hashing
Family of heat shock proteins
Chaperonins undergo large conformational changes during a folding reaction as a function of the enzymatic hydrolysis of ATP as well as binding of substrate
Chaperonin
Organ central to the nervous system
dominate the brain, it takes over functions from many other brain areas. In many mammals, the cerebral cortex consists of folded bulges called gyri that create
Brain
Plastic surgery procedure
employ small, horizontal incisions along the inframammary fold, in order to avoid redundant skin folds, especially in the reduction of very oversized breasts
Breast_reduction
Classification of a two-dimensional repetitive pattern
a digit, n, indicating the highest order of rotational symmetry: 1-fold (none), 2-fold, 3-fold, 4-fold, or 6-fold. The next two symbols indicate symmetries
Wallpaper_group
Protein family
N-terminal alpha/beta domain that binds and hydrolyzes nucleotides (a Rossmann fold) and a C-terminal alpha-helical domain. The N-terminal domain is 200-250
AAA_proteins
Polynomial sequence
development of a function of arbitrarily many variables according to higher-order Laplace functions], Journal für die Reine und Angewandte Mathematik (in German)
Hermite_polynomials
Full-sphere surround sound format
Sources in Higher-order Ambisonics, BBC R&D Publications, 2013 Johann-Markus Batke and Florian Keiler, Using VBAP-derived Panning Functions for 3D Ambisonics
Ambisonics
Probability distribution
\Pr[X_{1}+X_{2}\leq x]=F^{*2}(x)=\int _{0}^{x}F(x-y)\,dF(y),} and the n-fold convolution F ∗ n {\displaystyle F^{*n}} is defined inductively by the rule:
Heavy-tailed_distribution
Surgical procedure
2-fold more effective at identifying sperm in men with non-obstructive azoospermia. Compared with conventional TESE, micro-TESE has about 1.5-fold higher
Testicular_sperm_extraction
FOLD HIGHER-ORDER-FUNCTION
FOLD HIGHER-ORDER-FUNCTION
Girl/Female
British, English
Gold
Girl/Female
Shakespearean
The Merry Wives of Windsor' Mistress Ford.
Surname or Lastname
English
English : variant of Cordier.Catalan : occupational name for a maker of cord or string, from an agent derivative of Catalan corda ‘string’, ‘cord’.
Boy/Male
Biblical
A digger.
Girl/Female
British, English
Gold
Biblical
a digger
Surname or Lastname
English
English : variant of Highley.
Surname or Lastname
English
English : topographic name for someone who lived near a pen for animals, or an occupational name for someone who worked in one, from Middle English fold ‘pen’, ‘enclosure’ (Old English falod, fald).
Male
Swedish
Swedish form of Old Norse Dagr, DAGHER means "day."
Male
Swedish
Old Swedish form of Old Norse Oddr, ODDER means "point of a weapon."
Surname or Lastname
English
English : variant of Haggard.English : variant of Hager.
Surname or Lastname
English
English : from Middle English old, not necessarily implying old age, but rather used to distinguish an older from a younger bearer of the same personal name.North German form of Alt, like the English name a distinguishing name for the older of two bearers of a personal name.Americanized form of German Alt.
Surname or Lastname
English (mainly Sussex and Kent)
English (mainly Sussex and Kent) : topographic name from Middle English hilder ‘dweller on a slope’ (from Old English hylde ‘slope’).
Surname or Lastname
Jewish (Ashkenazic)
Jewish (Ashkenazic) : ornamental name from modern German Gold, Yiddish gold ‘gold’. In North America it is often a reduced form of one of the many compound ornamental names of which Gold is the first element.English and German : from Old English, Old High German gold ‘gold’, applied as a metonymic occupational name for someone who worked in gold, i.e. a refiner, jeweler, or gilder, or as a nickname for someone who either had many gold possessions or bright yellow hair.English : from an Old English personal name Golda (or the feminine Golde), which persisted into the Middle Ages as a personal name. The name was in part a byname from gold ‘gold’, and in part a short form of the various compound names with this first element.
Surname or Lastname
English
English : topographic name for someone who lived at the edge of a village or by some other boundary, Middle English border, from Old French bordure ‘edge’.
Male
English
English surname transferred to forename use, from the Old English word ford, FORD means "ford, river crossing."
Girl/Female
Muslim
Higher, Highest
Surname or Lastname
English
English : nickname from Middle English bold ‘courageous’, ‘daring’ (Old English b(e)ald, cognate with Old High German bald). In some cases it may derive from an Old English personal name (see Bald).English : topographic name for someone who lived or worked at the main house in a settlement, from Old English bold, the usual West Midland and northwestern form of Old English bÅðl, bÅtl ‘dwelling house’, ‘hall’.English : habitational name for someone from Bold in Lancashire, which is named with Old English bold ‘dwelling’, as in 2 above.German : from the Germanic personal name Baldo, a short form of the various compound names with the element bald ‘bold’, notably Baldwin in the north, and Reinbold in the south.Swedish : probably of German origin.
Boy/Male
American, British, English
Gold; Blond
Girl/Female
British, English
Gold
FOLD HIGHER-ORDER-FUNCTION
FOLD HIGHER-ORDER-FUNCTION
Surname or Lastname
English (Northumberland)
English (Northumberland) : variant of Brace.North German (also Bräss) : nickname from Middle Low German brÄs ‘noise’, ‘pomp’, a related form of brÄsch (see Braasch).German : topographic name from Brass ‘broom’, ‘gorse’, a common name element in the Lower Rhine and Ruhr.
Girl/Female
Gujarati, Hindu, Indian
Signifies Fear; Goddess Parvati
Boy/Male
Sikh
The light of Love
Male
Egyptian
, a Greco-Roman Egyptian name.
Boy/Male
Tamil
Simhikaprana | ஸீமà¯à®¹à¯€à®•à®¾à®ªà¯à®°à®¨à®¾
Bhanjana slayer of simhika
Boy/Male
American, Australian, British, Dutch, English, French, Latin
Son of Philip
Girl/Female
Indian
Sweet and Beautiful
Boy/Male
Hindu, Indian
Charming
Girl/Female
Tamil
Pradnaya | பà¯à®°à®¾à®¤à®¨à®¾à®¯à®¾
Knowledge, Wisdom, Buddhi
Surname or Lastname
English
English : occupational name from a late, extended form of Anglo-Norman French surgien ‘surgeon’.
FOLD HIGHER-ORDER-FUNCTION
FOLD HIGHER-ORDER-FUNCTION
FOLD HIGHER-ORDER-FUNCTION
FOLD HIGHER-ORDER-FUNCTION
FOLD HIGHER-ORDER-FUNCTION
n.
A flock of sheep; figuratively, the Church or a church; as, Christ's fold.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
v. t.
To confine in a fold, as sheep.
conj. Either
precedes two, or more, coordinate words or phrases, and is introductory to an alternative. It is correlative to or.
n.
To give an order to; to command; as, to order troops to advance.
a.
Applied to time: On the thither side of, older than; of more years than. See Hither, a.
n.
Rank; degree; thus, the order of a curve or surface is the same as the degree of its equation.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
v. i.
To become cold.
v. i.
To become folded, plaited, or doubled; to close over another of the same kind; to double together; as, the leaves of the door fold.
n.
A number of things or persons arranged in a fixed or suitable place, or relative position; a rank; a row; a grade; especially, a rank or class in society; a group or division of men in the same social or other position; also, a distinct character, kind, or sort; as, the higher or lower orders of society; talent of a high order.
v. t.
To lap or lay in plaits or folds; to lay one part over another part of; to double; as, to fold cloth; to fold a letter.
n.
Conformity with law or decorum; freedom from disturbance; general tranquillity; public quiet; as, to preserve order in a community or an assembly.
adv.
In a high manner, or to a high degree; very much; as, highly esteemed.
n.
A body of persons having some common honorary distinction or rule of obligation; esp., a body of religious persons or aggregate of convents living under a common rule; as, the Order of the Bath; the Franciscan order.
adv.
To this place; -- used with verbs signifying motion, and implying motion toward the speaker; correlate of hence and thither; as, to come or bring hither.
a.
Being on the side next or toward the person speaking; nearer; -- correlate of thither and farther; as, on the hither side of a hill.
v. i.
To confine sheep in a fold.
v. t.
To inclose within folds or plaitings; to envelop; to infold; to clasp; to embrace.
v. i.
To give orders; to issue commands.