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Effective particle coupling beyond tree level
In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory
Vertex_function
Polynomial function of degree two
vertex of a parabola is the place where it turns; hence, it is also called the turning point. If the quadratic function is in vertex form, the vertex
Quadratic_function
Topics referred to by the same term
surface Vertex function, describing the interaction between a photon and an electron Vertex (anatomy), the highest point of the head Vertex (gastropod):
Vertex
Japanese anime television series
Vertex Force (Japanese: バーテックスフォース, Hepburn: Bātekkusu Fōsu) is an original anime television series produced by SMDE [ja] and directed by Kazuhiro Takamura
Vertex_Force
Algebra used in 2D conformal field theories and string theory
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Vertex_operator_algebra
Renormalization scheme in quantum field theory
of Π ( 0 ) {\displaystyle \Pi (0)} . A similar reasoning using the vertex function leads to the renormalization of the electric charge e r {\displaystyle
On-shell renormalization scheme
On-shell_renormalization_scheme
Statistical mechanics model for crystal lattices
In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such
Ice-type_model
Type of discrete calculus
calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices and weights
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
Pictorial representation of the behavior of subatomic particles
meet at a vertex, which contributes a delta-function that ensures that the sum of the momenta are all equal. To compute a correlation function in the interacting
Feynman_diagram
Type of dominating set in graph theory
A Roman dominating function (RDF) is a function f : V → { 0 , 1 , 2 } {\displaystyle f:V\to \{0,1,2\}} such that for every vertex v {\displaystyle v}
Roman_dominating_set
Quantum field theory of electromagnetism
self-energy function Σ {\displaystyle \Sigma } One-loop contribution to the vertex function Γ {\displaystyle \Gamma } that, being closed loops, imply the presence
Quantum_electrodynamics
Type of program in computer graphics
shaders. The first shader-capable GPUs only supported pixel shading, but vertex shaders were quickly introduced once developers realized the power of shaders
Shader
service function inside UK utility company United Utilities, Vertex was spun out as a separate company in 1996. In 2007, United Utilities sold Vertex to a
Vertex_(company)
some fixed order). A vertex function fv for each vertex v. The vertex function maps the state of vertex v at time t to the vertex state at time t + 1 based
Graph_dynamical_system
energy; poles of this function determine the quasiparticle energy-momentum dispersion relation. The four-point vertex function Γ(K3,K4;K1,K2) describes
Pomeranchuk_instability
Feature of OpenGL for storing vertex data
via the Nvidia-created extension "vertex array range" or ATI's "vertex array object" extension. The following functions form the core of VBO access and
Vertex_buffer_object
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
Generalization of the ice-type (six-vertex) models
pairs of states. Each vertex j has an associated energy ϵj and Boltzmann weight wj=exp(−ϵjkBT) giving the partition function over the lattice as Z=∑exp(−∑jnjϵjkBT)
Eight-vertex_model
Method in physics used to deal with infinities
number of photons is zero. For example, at the one-loop order, the vertex function has both ultraviolet and infrared divergences. In contrast to the ultraviolet
Renormalization
Multivalued function in mathematics
number of trees with a designated root vertex is n n − 1 {\displaystyle n^{n-1}} . The exponential generating function of this counting sequence is: T ( x
Lambert_W_function
Deleting a graph edge and merging its nodes
f} be a function that maps every vertex in V ∖ { u , v } {\displaystyle V\setminus \{u,v\}} to itself, and otherwise, maps it to a new vertex w {\displaystyle
Edge_contraction
References Square brackets [ ] G[S] is the induced subgraph of a graph G for vertex subset S. Prime symbol ' The prime symbol is often used to modify notation
Glossary_of_graph_theory
Class of graph dynamical systems
some fixed order). A vertex function fi for each vertex i. The vertex function maps the state of vertex i at time t to the vertex state at time t + 1 based
Sequential_dynamical_system
Maximal biconnected subgraph
Specifically, it processes n vertex additions and m edge additions in O(m α(m, n)) total time, where α is the inverse Ackermann function. This time bound is proved
Biconnected_component
Theoretical physicist (1939–2023)
Thesis Nonperturbative solutions of the Bethe-Salpeter equation for the vertex function (1966) Doctoral advisor Hans Bethe Kenneth G. Wilson Doctoral students
Roman_Jackiw
On points of extreme curvature in curves
point of the curvature function a vertex. This theorem has many generalizations, including a version for space curves where a vertex is defined as a point
Four_vertex_theorem
parameter gradients between vertex attributes as a prerequisite for rasterization. Triangle setup unit A fixed-function unit in a GPU that performs triangle
Glossary_of_computer_graphics
Polynomial equation of degree two
for graphing a quadratic function. Since the graph is symmetric with respect to a vertical line through the vertex, the vertex's x-coordinate is located
Quadratic_equation
Component in electronic graphics processing units (GPUs)
The function of the vertex pipeline in any GPU is to take geometry data (usually supplied as vector points), work with it if needed with either fixed function
Vertex_pipeline
Fast-growing function
a simple subcubic graph (SSCG) is a finite simple graph in which each vertex has a degree of at most three. Suppose we have a sequence of simple subcubic
Friedman's_SSCG_function
S-shaped curve
and vertex at ( 2 , 1 ) {\displaystyle (2,1)} , corresponding to the range and midpoint ( 1 / 2 {\displaystyle 1/2} ) of the logistic function. Parametrically
Logistic_function
Path planning algorithm
A*. The only difference is the update _ vertex ( ) {\displaystyle {\text{update}}\_{\text{vertex}}()} function. Compared to A*, the parent of a node in
Theta*
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
In physics, proton and neutron magnetism
first-order and largest correction in QED, is found by calculating the vertex function shown in the diagram on the right. The calculation was discovered by
Nucleon_magnetic_moment
Type of field appearing in the Lagrangian
corresponding correlator obtained from F [ J ] {\displaystyle F[J]} , known as vertex function, is given by G Γ [ J ] N , c = δ Γ [ ϕ ¯ ] δ ϕ ¯ ( x 1 ) ⋯ δ ϕ ¯
Source_field
Value in quantum electrodynamics
mechanical correction—of the electron is found by calculating the vertex function shown in the adjacent diagram. The calculation is relatively straightforward
Anomalous magnetic dipole moment
Anomalous_magnetic_dipole_moment
Fractal creation method
polygon; the vertex is chosen at random in each iteration. Repeating this iterative process a large number of times, selecting the vertex at random on
Chaos_game
Monster and modular connection
moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James
Monstrous_moonshine
Methodic assignment of colors to elements of a graph
is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems
Graph_coloring
Dimensionality of space at which the character of the phase transition changes
invariance below this dimension. For small external wave vectors the vertex functions Γ {\displaystyle \Gamma } acquire additional exponents, for example
Critical_dimension
Real-time rendering technique
techniques use SH to encode multiple functions—usually the global lighting environment and a per-vertex radiance transfer function. The generalized lighting equation
Spherical_harmonic_lighting
Types of special mathematical functions
defined similarly to the gamma function but with different or "incomplete" integral limits. The usual gamma function is defined as an integral from zero
Incomplete_gamma_function
Length of shortest path between two nodes of a graph
over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph
Distance_(graph_theory)
Assignment of labels to elements of a graph
graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph. Likewise
Graph_labeling
Mathematical function
complete graph Kn + 1 for odd n. In such a graph, any single vertex v has n possible choices of vertex that it can be matched to, and once this choice is made
Double_factorial
Fundamental trigonometric functions
sine theorem Polar sine—a generalization to vertex angles Proofs of trigonometric identities Sinc function Sine and cosine transforms Sine integral Sine
Sine_and_cosine
Graphs of d-dimensional polytopes are d-connected
maximum of a linear function on a convex polytope (the linear programming problem). The simplex method starts at an arbitrary vertex of the polytope and
Balinski's_theorem
Directed graph with no directed cycles
vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed
Directed_acyclic_graph
Cloud-based service and infrastructure
February 2021 – Google Kubernetes Engine Autopilot is introduced. May 2021 – Vertex AI announced at Google.io June 2021 – In 2021, Apple was Google Cloud's
Google_Cloud_Platform
Identity in abelian theories due to gauge invariance
Clive Ward and Yasushi Takahashi to relate the wave function renormalization of the electron to its vertex renormalization factor, guaranteeing the cancellation
Ward–Takahashi_identity
Algorithm for maximum cardinality matching
and right sides of the bipartite graph and NIL is a special null vertex */ function BFS() is for each u in U do if Pair_U[u] = NIL then Dist[u] := 0 Enqueue(Q
Hopcroft–Karp_algorithm
Mathematical function with no sudden changes
In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies
Continuous_function
Generalization of finite element method
these functions restricted to a single element. All these functions are defined in the entire element interior. Vertex function. Edge function. Face function
Hp-FEM
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
Set of hypergraph nodes to which every hyperedge is connected
graph theory, a vertex cover in a hypergraph is a set of vertices, such that every hyperedge of the hypergraph contains at least one vertex of that set.
Vertex_cover_in_hypergraphs
Central object in linear algebra; mapping vectors to vectors
{e} _{2})&\cdots &T(\mathbf {e} _{n})\end{bmatrix}}} For example, the function T ( x ) = 5 x {\displaystyle T(x)=5x} is a linear transformation. Applying
Transformation_matrix
Shading language for WebGPU
@binding(0) var<uniform> mvp : mat4x4f; @vertex fn main(v_in : VertexInput) -> VertexOutput { var v_out : VertexOutput; v_out.clip_position = mvp * vec4f(v_in
WebGPU_Shading_Language
Plane curve: conic section
any parabola with the origin as vertex and the y axis as axis of symmetry can be considered as the graph of a function f ( x ) = a x 2 with a ≠ 0. {\displaystyle
Parabola
Figure formed by two rays meeting at a common point
line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and
Angle
Method for finding minimum spanning trees
the pseudocode below. function Prim(vertices, edges) is for each vertex in vertices do cheapestCost[vertex] ← ∞ cheapestEdge[vertex] ← null explored ← empty
Prim's_algorithm
Symmetric function invariant of graphs
G=(V,E)} with vertex set V = { v 1 , v 2 , … , v n } {\displaystyle V=\{v_{1},v_{2},\ldots ,v_{n}\}} , a vertex coloring is a function κ : V → C {\displaystyle
Chromatic_symmetric_function
Well-quasi-ordering of finite trees
{\displaystyle v} to w {\displaystyle w} is of length one (contains no other vertex). Take ( X , ≤ X ) {\displaystyle (X,\leq _{X})} to be a quasi-ordered (preordered)
Kruskal's_tree_theorem
Algorithm for finding shortest paths
v, then the distance of v is updated to alt. 1 function Dijkstra(Graph, source): 2 3 for each vertex v in Graph.Vertices: 4 dist[v] ← INFINITY 5 prev[v]
Dijkstra's_algorithm
Quantum field theory
to obtain all the n-point functions with perturbation theory. Using LSZ reduction formula we get from the n-point functions the corresponding process
Yang–Mills_theory
A vertex model is a type of statistical mechanics model in which the Boltzmann weights are associated with a vertex in the model (representing an atom
Vertex_model
Shading language
only included support for vertex shaders and pixel shaders ("fragment" in GLSL). A vertex shader is executed for each vertex that is submitted by the application
High-Level_Shader_Language
Coordinate system that is defined by points instead of vectors
but not at a vertex, one of the area coordinates λ 1...3 {\displaystyle \lambda _{1...3}} (the one associated with the opposite vertex) is zero, while
Barycentric_coordinate_system
Upper bound on intersecting set families
set. Because Kneser graphs have symmetries taking any vertex to any other vertex (they are vertex-transitive graphs), their fractional chromatic number
Erdős–Ko–Rado_theorem
Graph where all pairs of vertices are automorphic
the Rado graph Two countable vertex-transitive graphs are called quasi-isometric if the ratio of their distance functions is bounded from below and from
Vertex-transitive_graph
Set of edges without common vertices
common vertices. In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a largest matching
Matching_(graph_theory)
Method for solving quadratic equations
a < 0) of the quadratic function. One way to see this is to note that the graph of the function f(x) = x2 is a parabola whose vertex is at the origin (0, 0)
Completing_the_square
Every graph has evenly many odd vertices
class PPA encapsulates the difficulty of finding a second odd vertex, given one such vertex in a large implicitly-defined graph. An undirected graph consists
Handshaking_lemma
Cellular automaton
case, choose any unstable vertex ( x u , y u ) ∈ Γ {\displaystyle (x_{u},y_{u})\in \Gamma } at random. Topple this vertex by reducing its grain number
Abelian_sandpile_model
Putting fermions on a lattice with chiral symmetry results in more fermions than expected
theory with non-covariant contributions to the fermion self-energy and vertex function, rendering the theory non-renormalizable and difficult to work with
Fermion_doubling
Topics referred to by the same term
theory), a function used to solve a problem of optimal control for a dynamical system Hamiltonian path, a path in a graph that visits each vertex exactly
Hamiltonian
Shading algorithm in computer graphics
in OpenGL and Direct3D's fixed-function pipeline (before Direct3D 10 and OpenGL 3.1), and is carried out on each vertex as it passes down the graphics
Blinn–Phong_reflection_model
Node ordering for directed acyclic graphs
ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of
Topological_sorting
Binary tree of rational numbers
parents of a vertex. Each vertex a/b has one child whose value is less than 1, a/a + b (because a + b > a). Similarly, each vertex a/b has one
Calkin–Wilf_tree
Unproven computational hardness assumption
Hamiltonian cycles, maximum cliques, maximum independent sets, and vertex cover on n-vertex graphs. Conversely, if any of these problems has a subexponential
Exponential_time_hypothesis
Method to solve optimization problems
a vertex of the polytope and then walking along a path on the edges of the polytope to vertices with non-decreasing values of the objective function until
Linear_programming
Object relationship in programming language
insert(vertex.get()); } void removeVertex(SharedPtr<Vertex> vertex) { vertices.erase(vertex); } void addEdge(SharedPtr<Vertex> from, SharedPtr<Vertex> to)
Friend_class
Path in a graph that visits each vertex exactly once
directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian
Hamiltonian_path
Graph with at most one cycle per component
pairs of vertices, such that no two cycles of consecutive edges share any vertex with each other, nor can any two cycles be connected to each other by a
Pseudoforest
n-vertex cubic graph? The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Type of computer science algorithm
simply start at one vertex and perform a random walk of about 20n3 steps, the chance that we will stumble across the other vertex provided that it is
In-place_algorithm
Arithmetic operation
circle of the complex plane at the vertices of a regular n-gon with one vertex on the real number 1. As the number e2kπi/n is the primitive nth root of
Exponentiation
Maximum size of an independent set of the matroid
Then the rank function r(B) is the number of vertices in the graph, minus the number of connected components of B (including single-vertex components).
Matroid_rank
Algorithm for finding the shortest paths in graphs
algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's
Bellman–Ford_algorithm
Algorithm to search the nodes of a graph
and it checks whether a vertex has been explored before enqueueing the vertex rather than delaying this check until the vertex is dequeued from the queue
Breadth-first_search
Partition of a graph's nodes into 2 disjoint subsets
some cases cuts are identified with their cut-sets rather than with their vertex partitions. In a flow network, an s–t cut is a cut that requires the source
Cut_(graph_theory)
Upper bound on a graph's Shannon capacity
(G)\vartheta ({\bar {G}})\geq n,} with equality if G {\displaystyle G} is vertex-transitive. The Lovász "sandwich theorem" states that the Lovász number
Lovász_number
GPU for mobile devices, used by Nintendo on their 3DS consoles
low power fixed-function "MAESTRO" GPU architecture. The PICA200 implements the "MAESTRO-2G" architecture and supports programmable vertex shaders and geometry
PICA200
Graphics libraries API design pattern
when used in conjunction with immediate mode rendering systems. Primitive vertex attribute data may be inserted frame by frame into a command buffer by a
Immediate mode (computer graphics)
Immediate_mode_(computer_graphics)
theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector
Edge_and_vertex_spaces
Algorithmic technique
vertex of degree greater than k {\displaystyle k} , remove v {\displaystyle v} from the graph and decrease k {\displaystyle k} by one. Every vertex cover
Kernelization
Terminology used in computer graphics
In computer graphics, fixed-function is a term primarily used to describe 3D graphics APIs and GPUs designed prior to the advent of programmable shaders
Fixed-function (computer graphics)
Fixed-function_(computer_graphics)
Construction for n-dimensional noise functions
Simplex noise is the result of an n-dimensional noise function comparable to Perlin noise ("classic" noise) but with fewer directional artifacts, in higher
Simplex_noise
Triangular array of the binomial coefficients
a vertex V, there is one vertex at distance 0 from V (that is, V itself), three vertices at distance 1, three vertices at distance √2 and one vertex at
Pascal's_triangle
Shape with three sides
an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the
Triangle
perfect matching) has a vertex cover of size n + k {\displaystyle n+k} . The odd cycle transversal can be transformed into a vertex cover by including both
Odd_cycle_transversal
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VERTEX FUNCTION
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