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Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation
Function_representation
Process by which a quantum system takes on a definitive state
also called the "position representation". When the wave function representation is used, the "reduction" is called "wave function collapse". The Schrödinger
Wave_function_collapse
Second-order control system
{x}}}{dt}}={\begin{bmatrix}{\dot {q}}\\{\ddot {q}}\\\end{bmatrix}}} In this representation, it is clear that the control input u {\displaystyle {\textbf {u}}}
Double_integrator
Theorem in economics
utility representation theorem shows that, under certain conditions, a preference ordering can be represented by a real-valued utility function, such that
Utility representation theorem
Utility_representation_theorem
Concept in economics
real-valued range. That is, there is no real-valued representation of a preference relation by a utility function, whether continuous or not. Lexicographic preferences
Lexicographic_preferences
Method of representing a 3D object by defining the limits of its volume
surface Function representation Geometric modeling kernel NURBS Spline Non-photorealistic rendering – Style of rendering "Boundary representation" (PDF)
Boundary_representation
Representation on functions in computer engineering
engineering, and computer science, a function model or functional model is a structured representation of the functions (activities, actions, processes, operations)
Function_model
Mathematical function for the probability a given outcome occurs in an experiment
likely different results are. Formally, it is a probability measure: a function that assigns probabilities to events in a way that satisfies the axioms
Probability_distribution
Topics referred to by the same term
a type of key on computer keyboards Function model, a structured representation of processes in a system Function object or functor or functionoid, a
Function
Type of generalization of periodic functions in Euclidean space
ideal (or an abstracted irreducible fundamental representation). As mentioned, automorphic functions can be seen as generalizations of modular forms (as
Automorphic_form
Real-valued mathematical function
(AND). R-functions are used in computer graphics and geometric modeling in the context of implicit surfaces and the function representation. They also
Rvachev_function
Type of artificial neural network architecture
the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds
Kolmogorov–Arnold_Networks
Voting system that makes outcomes proportional to vote totals
Proportional representation (PR) is achieved by any electoral system under which subgroups of an electorate are reflected proportionately in the elected
Proportional_representation
Particular representation of a signal
analytic representation of a real-valued function is an analytic signal, comprising the original function and its Hilbert transform. This representation facilitates
Analytic_signal
Representation of a mathematical function
graphical representation of the graph of a function is also known as a plot. In the case of functions of two variables – that is, functions whose domain
Graph_of_a_function
Mathematical description of quantum state
is a corresponding representation that is associated to a function space of wave functions. Between all these different function spaces and the abstract
Wave_function
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Counterexample to the converse of the intermediate value theorem
3629256 has the base-13 representation 9+0−−7. Conway's base-13 function takes in a real number x and considers its base-13 representation as a sequence of symbols
Conway's_base_13_function
Restricted representation Group representation Group ring Maschke's theorem Regular representation Character (mathematics) Character theory Class function Representation
List of representation theory topics
List_of_representation_theory_topics
Extension of the factorial function
}{\frac {t^{s}}{e^{t}-1}}\,{\frac {dt}{t}}} an integral representation for the log-gamma function is: l o g Γ ( z + 1 ) = − γ z + ∫ 0 ∞ e − z t − 1 +
Gamma_function
Analytic function in mathematics
Riemann zeta function, or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ {\displaystyle \zeta } (zeta), is a function of a complex
Riemann_zeta_function
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
physical constants Particular values of the Riemann zeta function Particular values of the gamma function Physical constant Both i and −i are roots of this equation
List of mathematical constants
List_of_mathematical_constants
that the Jacobi theta function is invariant under the action of a discrete subgroup of the Heisenberg group. The representation was popularized by David
Theta_representation
Set of functions between two fixed sets
representation. For (not necessarily continuous) functions, there is the exponential law that relates functions on a product on one hand and function-valued
Function_space
Mathematical transform that expresses a function of time as a function of frequency
the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the
Fourier_transform
especially in the fields of group theory and representation theory of groups, a class function is a function on a group G that is constant on the conjugacy
Class_function
Branch of mathematics that studies abstract algebraic structures
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of
Representation_theory
Mathematical representation in functional analysis
Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric isomorphism. In the former
Gelfand_representation
Set of learning techniques in machine learning
problem is formulated, where the objective function consists of the classification error, the representation error, an L1 regularization on the representing
Representation_learning
Data structure for Boolean functions
is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other
Binary_decision_diagram
descriptions of real objects. By utilizing technologies such as Function representation (FRep) it becomes possible to compactly describe and understand
Digital_materialization
Mathematical function
If the real part of z is positive then the digamma function has the following integral representation due to Gauss: ψ ( z ) = ∫ 0 ∞ ( e − t t − e − z t
Digamma_function
Type of function in database management
In database management, an aggregate function or aggregation function is a function where multiple values are processed together to form a single summary
Aggregate_function
Symbolic boolean function representation, extension of BDDs
ADD can also be seen as a Boolean function, or a vectorial Boolean function, by extending the codomain of the function, such that f:{0,1}n→Q with S⊆Q and
Algebraic_decision_diagram
Power series derived from a discrete probability distribution
generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random
Probability generating function
Probability_generating_function
are preference representation theorems—statements about the representation of a preference ordering by a real-valued utility function. The theorems were
Debreu's representation theorems
Debreu's_representation_theorems
Function in harmonic analysis on groups
decomposition of the unitary representation of G on L2(G/K). In this case the commutant of G is generated by the algebra of biinvariant functions on G with respect
Zonal_spherical_function
Integral transform and linear operator
with the function 1 / ( π t ) {\displaystyle 1/(\pi t)} (see § Definition). The Hilbert transform has a particularly simple representation in the frequency
Hilbert_transform
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Computational physics simulation tool
Quasiprobability distribution § Characteristic functions Nonclassical light Glauber–Sudarshan P-representation Wehrl entropy Kôdi Husimi (1940). "Some Formal
Husimi_Q_representation
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is a real-valued function of a real variable that can be defined as: f ( x ) = { 1 q if x = p q ( x is rational), with p ∈ Z and
Thomae's_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
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
Derived representation of a digital image
meshes, e.g. by the marching cubes algorithm. Signed distance function Function representation Parallel curve Level sets methods for distance computation
Distance_transform
Function in analytic number theory
involving the eta function can be listed. The first one follows from a change of variable of the integral representation of the Gamma function (Abel, 1823)
Dirichlet_eta_function
Special mathematical function defined as sin(x)/x
an absolute maximum at ξ0 = (0, 1). The normalized sinc function has a simple representation as the infinite product: sin ( π x ) π x = ∏ n = 1 ∞ (
Sinc_function
Number of partitions of an integer
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because
Partition function (number theory)
Partition_function_(number_theory)
Polynomial sequence
} From the generating-function representation above, we see that the Hermite polynomials have a representation in terms of a contour integral
Hermite_polynomials
Deliberative assembly that makes laws
Althing, founded in 930 CE. Democratic legislatures have six major functions: representation, deliberation, legislation, authorizing expenditure, making governments
Legislature
Function defined by multiple sub-functions
mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned
Piecewise_function
Multivariate functions can be written using univariate functions and summing
theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [ 0 , 1 ] n → R {\displaystyle
Kolmogorov–Arnold representation theorem
Kolmogorov–Arnold_representation_theorem
Generalized function whose value is zero everywhere except at zero
the role of the Cauchy integral. Another representation of the delta function in a space of holomorphic functions is on the space H ( D ) ∩ L 2 ( D ) {\displaystyle
Dirac_delta_function
Field of artificial intelligence
Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems whereas
Knowledge representation and reasoning
Knowledge_representation_and_reasoning
Type of Dirichlet series associated to number field extensions
prime ideals, that for the trivial representation of the Galois group, the Artin L-function is the Dedekind zeta function of the smaller field: L ( s , 1
Artin_L-function
Mathematical function
In mathematics, the trigamma function, denoted ψ1(z) or ψ(1)(z), is the second of the polygamma functions, and is defined by ψ 1 ( z ) = d 2 d z 2 ln
Trigamma_function
Smooth approximation of one-hot arg max
arg max as a function with categorical output 1,…,n (corresponding to the index), consider the arg max function with one-hot representation of the output
Softmax_function
Non-cryptographic hash function
Fowler–Noll–Vo (or FNV) is a non-cryptographic hash function created by Glenn Fowler, Landon Curt Noll, and Kiem-Phong Vo. The basis of the FNV hash algorithm
Fowler–Noll–Vo_hash_function
Conjectures connecting number theory and geometry
representation of G and every finite-dimensional representation of LG, he defines an L-function. One of his conjectures states that these L-functions
Langlands_program
others, found connections with combinatorics, representation theory and cohomology. A Hessenberg function is a map h : { 1 , 2 , … , n } → { 1 , 2 , …
Hessenberg_variety
In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system Δ {\displaystyle
Kostant_partition_function
Group homomorphism into the general linear group over a vector space
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector
Group_representation
Concept in statistics
regularized version of the empirical characteristic function. The characteristic-function representation can be used directly for quantum-state reconstruction
Kernel_density_estimation
Surface representing points of constant value within a volume
visualisation. A more general way to construct an isosurface is to use the function representation. Surface of constant pressure. Surface with shading information
Isosurface
Ratio of polynomial functions
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator
Rational_function
Artificial neural network node function
In artificial neural networks, the activation function of a node is a function that calculates the output of the node based on its individual inputs and
Activation_function
Topics referred to by the same term
Green function might refer to: Green's function of a differential operator Deligne–Lusztig theory (Green function) in the representation theory of finite
Green_function
Mathematical function resembling a boxcar
boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant A. The function is named
Boxcar_function
forms a representation of a subgroup using a known representation of the whole group. Restriction is a fundamental construction in representation theory
Restricted_representation
Signal representation
frequency-domain representation of the signal. The inverse Fourier transform converts the frequency-domain function back to the time-domain function. A spectrum
Frequency_domain
Representation theory of the symplectic group
In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David
Oscillator_representation
Indicator function of positive numbers
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside
Heaviside_step_function
Functional relationship between two quantities
(mass) function directly, these methods introduce an implicit bias in the representation of the data, and thus should be avoided. The survival function, on
Power_law
Function specifying the behavior of a component in an electronic or control system
a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models
Transfer_function
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
character is a one-dimensional representation. 2. The character of a finite-dimensional representation π is the function g ↦ tr π ( g ) {\displaystyle
Glossary of representation theory
Glossary_of_representation_theory
Number with a real and an imaginary part
V(t) is called the analytic representation of the real-valued, measurable signal v(t). In fluid dynamics, complex functions are used to describe potential
Complex_number
Concept in mathematical group theory
more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace
Character_theory
Group in mathematical representation theory
linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and is
Metaplectic_group
Hash function without any collisions
perfect hash functions are the evaluation time, which should be constant, the construction time, and the representation size. A perfect hash function with values
Perfect_hash_function
Element of a basis for a function space
basis functions. In finite-dimensional vector spaces, this representation is purely algebraic and involves only finitely many basis functions, whereas
Basis_function
Visual artifact that depicts or records perception
processing, a picture function is a mathematical representation of a two-dimensional image as a function of two spatial variables. The function f(x,y) describes
Image
Special mathematical functions defined on the surface of a sphere
function composition ψ ↦ ψ ∘ ρ − 1 {\displaystyle \psi \mapsto \psi \circ \rho ^{-1}} for ψ a spherical harmonic and ρ a rotation. The representation
Spherical_harmonics
Inverse functions of sin, cos, tan, etc.
trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions, under
Inverse trigonometric functions
Inverse_trigonometric_functions
Concept in mathematics
In mathematics, the layer cake representation of a non-negative, real-valued measurable function f {\displaystyle f} defined on a measure space ( Ω ,
Layer_cake_representation
Special function of two variables
real analytic Eisenstein series is a special function of two variables that is used in the representation theory of SL(2, R) and, more broadly, in analytic
Real analytic Eisenstein series
Real_analytic_Eisenstein_series
Artin as an expression appearing in the functional equation of an Artin L-function. Suppose that L {\displaystyle L} is a finite Galois extension of the local
Artin_conductor
Mathematical software
rational function representation—similar to ALPAK—which processed ratios of multivariable polynomials with integer coefficients. This representation relied
Computer_algebra_system
Mathematical approach to quantum optics
P representation has the peculiarity that it is not always positive, and is not a bona-fide probability function. We wish to construct a function P (
Glauber–Sudarshan P representation
Glauber–Sudarshan_P_representation
mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a
Representation_ring
Type of group and algebra representation
thought of as a function (a homomorphism) from a group into a set of invertible matrices and in this context is called a matrix representation. However, it
Irreducible_representation
\rho } may lead to the same f {\displaystyle f} . That is, the representation of a function as an infinite-width neural network is not unique. However, among
Barron_space
Response of an optical system to a point source of light
The point spread function (PSF) describes the response of a focused optical imaging system to an idealized point source of light. In casual terms, for
Point_spread_function
Property of an intermediate representation in a compiler
apply to the other. Using CPS as the intermediate representation is more natural for higher-order functions and interprocedural analysis. CPS also easily
Static_single-assignment_form
Representation of the symmetry group of spacetime in special relativity
n-dimensional representation, and Π is a possibly infinite-dimensional representation. A special case of this construction is when V is a space of functions defined
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
American mathematician
the areas of analytic number theory, automorphic forms and representation theory, L-functions, harmonic analysis, and homogeneous dynamics. Kontorovich
Alex_Kontorovich
Quantum physics terminology
finite region R ⊂ X {\displaystyle R\subset X} . Using a wave function representation, for example, this means 0 = lim R → ∞ P ( particle measured inside
Bound_state
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FUNCTION REPRESENTATION
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FUNCTION REPRESENTATION
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FUNCTION REPRESENTATION
FUNCTION REPRESENTATION
FUNCTION REPRESENTATION
FUNCTION REPRESENTATION
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