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Machine learning engine service
single system. At launch, Google claimed that Vertex AI required roughly 80% fewer lines of code to train a model compared to competing platforms. In June
Gemini Enterprise Agent Platform
Gemini_Enterprise_Agent_Platform
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
the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced
Ice-type_model
Generalization of the ice-type (six-vertex) models
In statistical mechanics, the eight-vertex model is a generalization of the ice-type (six-vertex) models. It was discussed by T. Bill Sutherland and C
Eight-vertex_model
Statistical model in quantum mechanics of magnetic materials
six-vertex model, after identifying γ = 2 η {\displaystyle \gamma =2\eta } , where η {\displaystyle \eta } is the anisotropy parameter of the six-vertex model
Quantum_Heisenberg_model
Topics referred to by the same term
Look up vertex in Wiktionary, the free dictionary. Vertex, vertices or vertexes may refer to: Vertex (geometry), a point where two or more curves, lines
Vertex
Set of polygons to define the surface of a 3D model
Face-vertex meshes improve on VV mesh for modelling in that they allow explicit lookup of the vertices of a face, and the faces surrounding a vertex. The
Polygon_mesh
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
Spin model on a planar lattice
generalization of the Potts model, and as with the Potts model, the model is defined by configurations which are assignments of spins to each vertex of a graph, where
Chiral_Potts_model
Australian physicist (1940–2025)
solved models, in particular vertex models such as the six-vertex model and eight-vertex model, and the chiral Potts model and hard hexagon model. A recurring
Rodney_Baxter
Mathematical model
condensation to compute a determinant. They are also closely related to the six-vertex model with domain wall boundary conditions from statistical mechanics. They
Alternating_sign_matrix
GPU whose shading hardware has equal capabilities for all stages of rendering
abstractions (such as Shader Model 1.x) used very different instruction sets for vertex shaders and pixel shaders, with vertex shaders having a much more
Unified_shader_model
XXZ spin chain XYZ spin chain 6-vertex model 8-vertex model Kondo Model Anderson impurity model Chiral Gross–Neveu model Ishimori equation Kadomtsev–Petviashvili
List_of_integrable_models
Large language model developed by Google
which Google intended to make available to clients through Google Cloud's Vertex AI service. The publication also stated that Google was arming Gemini to
Gemini_(language_model)
Shading language
vertex shader, their output position is interpolated to form pixels within its area; this process is known as rasterization. DirectX 10 (Shader Model
High-Level_Shader_Language
Gauge theory providing unifying formalism for integrable systems
lattice models such as the six-vertex model of Lieb and the Heisenberg spin chain and integrable field theories such as principal chiral models, symmetric
Four-dimensional Chern–Simons theory
Four-dimensional_Chern–Simons_theory
Type of program in computer graphics
rasterizer. Vertex shaders can enable powerful control over the details of position, movement, lighting, and color in any scene involving 3D models. Geometry
Shader
Property of certain dynamical systems
solutions are examples. 8-vertex model Ice-type model of Lieb Gaudin model Ising model in 1- and 2-dimensions ZN model (or clock model) in 1- and 2-dimensions
Integrable_system
Geometry definition file format
geometry alone – namely, the position of each vertex, the UV position of each texture coordinate vertex, vertex normals, and the faces that make each polygon
Wavefront_.obj_file
Topological quantum field theory
lattice models (like the six-vertex model or the XXZ spin chain), integrable quantum field theories (such as the Gross–Neveu model, principal chiral model and
Chern–Simons_theory
Shading algorithm in computer graphics
a shading model used 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
Blinn–Phong_reflection_model
Physical model defined on a lattice
field theory. Ising model ANNNI model Potts model Chiral Potts model XY model Classical Heisenberg model n-vector model Vertex model Toda lattice cellular
Lattice_model_(physics)
Representation of a 3D object with only its edges rendered
two tables: (1) Vertex Table, and, (2) Edge Table. The vertex table consists of three-dimensional coordinate values for each vertex with reference to
Wire-frame_model
Image-generating machine learning model
users with a Google account through services including Gemini, ImageFX, and Vertex AI. Imagen's original version was first presented in a paper published in
Imagen_(text-to-image_model)
American mathematician and mathematical physicist
doctoral dissertation. The title was Asymptotic Phenomena in the Six-Vertex Model. He joined the Columbia University mathematics department in 2020. He
Amol_Aggarwal
American physicist
career he solved the six vertex model and developed an exact solution in 1967, which he then followed with the eight vertex model in 1970. He completed his
T._Bill_Sutherland
Theory of forces and subatomic particles
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions
Standard_Model
Method for finding the exact solution of certain quantum mechanics models
model Gaudin model XXX and XXZ Heisenberg spin chain for arbitrary spin s {\displaystyle s} Hubbard model Kondo model Lieb–Liniger model Six-vertex model
Bethe_ansatz
Cellular automaton
of times each vertex topples during each iteration is also independent of the choice of toppling order. To generalize the sandpile model from the rectangular
Abelian_sandpile_model
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
Two closely related models for generating random graphs
fixed vertex set with a fixed number of edges are equally likely. In the model introduced by Gilbert, also called the Erdős–Rényi–Gilbert model, each
Erdős–Rényi_model
Notation for a polyhedron's vertex figure
variously been called a vertex description, vertex type, vertex symbol, vertex arrangement, vertex pattern, face-vector, vertex sequence. It is also called
Vertex_configuration
Type of model in quantum statistical physics
variations of the Heisenberg model (XXZ, XYZ), and even in statistical lattice theory, such as for the six-vertex model. Another spin chain with physical
Spin_chain
onto a rotated 3D model, such as zbrush or mudbox, also sometimes able to modify vertex attributes. 3D scene A collection of 3D models and lightsources
Glossary_of_computer_graphics
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
Polytope or tiling whose vertices are identical
is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by
Isogonal_figure
Method used to solve integrable many-body quantum systems
integrable models were obtained in 1989. Essential progress was achieved in study of ice-type models: the bulk free energy of the six vertex model depends
Quantum inverse scattering method
Quantum_inverse_scattering_method
Shape made by slicing off a corner of a polytope
geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a general n-polytope is sliced off. Take some corner or vertex of a polyhedron
Vertex_figure
Point of extreme curvature on a curve
In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of
Vertex_(curve)
Nonlinear partial differential equation
quantum sine-Gordon equation should be modified so the exponentials become vertex operators L Q s G = 1 2 ∂ μ φ ∂ μ φ + 1 2 m 0 2 φ 2 − α ( V β + V − β )
Sine-Gordon_equation
Mathematical models representing biological cells
the individual cells. Examples of off-lattice models are center-based models, vertex-based models, models based on the immersed boundary method and the
Cell-based_models
polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows
List_of_uniform_polyhedra
Interpolation technique for surface shading
vertex normals. The surface normal is interpolated and normalized at each pixel and then used in a reflection model, e.g. the Phong reflection model,
Phong_shading
quantum double model can be generalized to the case where the input data is given by a C* Hopf algebra. In this case, the face and vertex operators are
Quantum_double_model
Graph generated by a random process
Another model, which generalizes Gilbert's random graph model, is the random dot-product model. A random dot-product graph associates with each vertex a real
Random_graph
Scale-free network generation algorithm
The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and
Barabási–Albert_model
Procedure to convert 3D scenes to 2D images
usually larger than available onboard memory. The geometry pipeline and the vertex pipeline are responsible for most of the operations with polygons. These
Graphics_pipeline
American mathematician (born 1964)
YouTube. Rio ICM2018. October 17, 2018. "Richard Kenyon: "On the 5-Vertex Model"". YouTube. Institute for Pure & Applied Mathematics (IPAM). July 27
Richard_Kenyon
Polyhedra in which all vertices are the same
set of thirteen convex polyhedra whose faces are regular polygons and are vertex-transitive,[citation needed] although they are not face-transitive and are
Archimedean_solid
Model for representing text documents
Vector space model (VSM) or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the
Vector_space_model
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
Algorithm for finding shortest paths
the path from the given vertex to the source). The code u ← vertex in Q with min dist[u], searches for the vertex u in the vertex set Q that has the least
Dijkstra's_algorithm
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)
Regular infinite tree structure used in statistical mechanics
convenient to mark a given vertex as the root, to be used as a reference point when considering local properties of the graph. Once a vertex is marked as the root
Bethe_lattice
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
Interpolation method in computer graphics
vertex in a polygonal 3D model is either specified for each vertex or found by averaging the surface normals of the polygons that meet at each vertex
Gouraud_shading
Limit of a constant-density system of particles as its volume increases
some models of statistical mechanics, the thermodynamic limit exists, but depends on boundary conditions. For example, this happens in six vertex model: the
Thermodynamic_limit
Depicting depth with levels of darkness
each polygon vertex. Apply an illumination model to each vertex to calculate the light intensity from the vertex normal. Interpolate the vertex intensities
Shading
Model of mesons in the massless quark limit
In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the
Chiral_model
Quantum consistency equation
model in 1944. The hunt for solvable lattice models has been actively pursued since then, culminating in Rodney Baxter's solution of the eight vertex
Yang–Baxter_equation
rule allows a subject to create new objects (add a vertex and an edge from the subject to the new vertex) remove rule allows a subject to remove rights it
Take-grant_protection_model
Directional vector associated with a vertex
explicitly for artistic purposes. Vertex normals are used in Gouraud shading, Phong shading and other lighting models. Using vertex normals, much smoother shading
Vertex_normal
Solid with six equal square faces
number of vertices, edges, and faces. All three square faces surrounding a vertex are orthogonal to each other, meaning the planes are perpendicular, forming
Cube
Russian physicist and mathematician
Together with Anatoly Izergin, he discovered the 19-vertex model (sometimes called the Izergin-Korepin model). In 1993, together with A. R. Its, Izergin and
Vladimir_Korepin
alternating sign matrix in the solution of ice-type models. The corresponding ice-type model is the six vertex model with domain wall boundary conditions. Mathematical
Combinatorics_and_physics
American mathematical physicist
the six-vertex model of ice in two dimensions, the one-dimensional delta Bose gas (now called the Lieb-Liniger model) and the Hubbard model. Together
Elliott_H._Lieb
maximum GV/s for Vertex Shader's performance compared to the theoretical maximum as it is more realistic for real world applications. This model is also known
List of Nvidia graphics processing units
List_of_Nvidia_graphics_processing_units
Deleting a graph edge and merging its nodes
Edge contraction is a fundamental operation in the theory of graph minors. Vertex identification is a less restrictive form of this operation. The edge contraction
Edge_contraction
Object modeling method
representations used in ray tracers. The basic object used in mesh modeling is a vertex, a point in three-dimensional space. Two vertices connected by a
Polygonal_modeling
3D model's surface projected to a 2D image
When a model is created as a polygon mesh using a 3D modeller, UV coordinates (also known as texture coordinates) can be generated for each vertex in the
UV_mapping
Series of GPUs by Nvidia
Manufacturing process: 90 nm Core Clock: 425 MHz Vertex Processors: 1 Pixel Pipelines: 2 Shader Model: 3 DirectX support: v9.0c Video playback acceleration:
GeForce_6_series
Mathematical model of waves on a shallow water surface
is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical
Korteweg–De_Vries_equation
Mathematics of a particle physics model
The Standard Model of particle physics is a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1)
Mathematical formulation of the Standard Model
Mathematical_formulation_of_the_Standard_Model
Network whose degree distribution follows a power law
the couple of vertices. Rather, for every vertex j there is an intrinsic fitness xj and a link between vertex i and j is created with a probability p (
Scale-free_network
Method for solving certain nonlinear partial differential equations
statistical lattice models Ising model in one- and two-dimensions Square ice model Eight-vertex model Hard hexagon model Chiral Potts model Exactly solvable
Inverse_scattering_transform
Color model based on red, green and blue
For the RGB model, this is represented by a cube using non-negative values within a 0–1 range, assigning black to the origin at the vertex (0, 0, 0), and
RGB_color_model
Model of web browser usage
edges. Models start with a single node v 0 {\displaystyle v_{0}} and have k {\displaystyle k} self-loops. v t {\displaystyle v_{t}} denotes a vertex added
Random_surfing_model
two disjoint sets of vertices with the condition that no vertex is connected to another vertex of the same set. In FMC diagrams, members of one set are
Fundamental_modeling_concepts
Open-source machine learning platform
adopted the Kubeflow Pipelines DSL within its Vertex AI Pipelines product. For certain machine learning models and libraries, the Kubeflow Training Operator
Kubeflow
Mathematical model of ferromagnetism in statistical mechanics
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical
Ising_model
Any of the five regular polyhedra
congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: a regular tetrahedron (four triangular
Platonic_solid
American electric vehicle and clean energy company
first car model, the Roadster sports car, in 2008; the Model S sedan in 2012; the Model X SUV in 2015; the Model 3 sedan in 2017; the Model Y crossover
Tesla,_Inc.
Adjacent subset of an undirected graph
independent set in a single vertex. An interval graph is a graph whose maximal cliques can be ordered in such a way that, for each vertex v, the cliques containing
Clique_(graph_theory)
Vertex adjacent to all others in a graph
universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating vertex, as it
Universal_vertex
infinitely many triangular tilings existing around each vertex in an octagonal tiling vertex figure. It is a part of a sequence of regular honeycombs
Order-8-3 triangular honeycomb
Order-8-3_triangular_honeycomb
Quantum number related to the strong force
charge, two gluons can also interact. A typical interaction vertex (called the three gluon vertex) for gluons involves g + g → g. This is shown here, along
Color_charge
Vertices connected in pairs by edges
and v and to be incident on them. A vertex may belong to no edge, in which case it is not joined to any other vertex and is called isolated. When an edge
Graph_(discrete_mathematics)
Type of integrable system
spectral curves. (The Garnier system is the classical limit of the Gaudin model. In turn, the Schlesinger equations are the classical limit of the Knizhnik–Zamolodchikov
Hitchin_system
Machine learning model
model is a machine learning model which takes an input natural language prompt and produces an image matching that description. Text-to-image models gradually
Text-to-image_model
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
Probabilistic model
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional
Graphical_model
infinitely many triangular tilings existing around each vertex in a heptagonal tiling vertex figure. It a part of a sequence of self-dual regular honeycombs:
Order-7-3 triangular honeycomb
Order-7-3_triangular_honeycomb
Theorem of dynamical systems
statistical lattice models Ising model in one- and two-dimensions Square ice model Eight-vertex model Hard hexagon model Chiral Potts model Exactly solvable
Liouville–Arnold_theorem
Generalization of graph theory
to model Horn-satisfiability. Many theorems and concepts involving graphs also hold for hypergraphs, in particular: Matching in hypergraphs; Vertex cover
Hypergraph
Archimedean solid with 62 faces
right amount, rotating each face so that each triangle vertex continues to touch a pentagon vertex, without changing the size of the faces, and patching
Rhombicosidodecahedron
Length of shortest path between two nodes of a graph
graph. A central vertex in a graph of radius r is one whose eccentricity is r—that is, a vertex whose distance from its furthest vertex is equal to the
Distance_(graph_theory)
Integrable classical system
structure of quantum Gaudin models. In particular, Feigin, Frenkel and Reshetikhin studied them using the theory of vertex operator algebras, showing the
Garnier_integrable_system
Grand Unified Theory proposed in 1974
Georgi–Glashow model is a particular Grand Unified Theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model, the Standard Model gauge
Georgi–Glashow_model
Statistical tool to model changing systems
random variable. Modeling a problem as a Markov random field is useful because it implies that the joint distributions at each vertex in the graph may
Markov_model
File format for 3D printing and scanning
represented as follows: facet normal ni nj nk outer loop vertex v1x v1y v1z vertex v2x v2y v2z vertex v3x v3y v3z endloop endfacet where each n or v is a floating-point
STL_(file_format)
VERTEX MODEL
VERTEX MODEL
Surname or Lastname
English (Kent and London)
English (Kent and London) : from Old French verge ‘half-acre’, hence a status name for the owner of that amount of land.Catalan (Vergé) : variant of Verger, topographic name from Catalan verger ‘orchard’ (Latin viridiarium)Catalan : possibly also a nickname from verge ‘maiden’ (Latin virgo ‘maiden’).
Surname or Lastname
English
English : variant of Varley.Dutch : reduced form of van der Leye, a topographic name for someone living near the river Leie.French : habitational name from a place called Verlée in Liège province, Belgium.
Male
German
Low German form of French Martin, MERTEN means "of/like Mars."
Female
Hebrew
(וֶרֶד) Hebrew unisex name VERED means "rose."
Boy/Male
Swedish American Teutonic
Friend protector.
Boy/Male
Australian, Danish, Dutch, Finnish, German, Swedish, Teutonic
Army Defender; Army Warrior
Male
Scandinavian
Scandinavian form of German Werner, VERNER means "Warin warrior," i.e. "covered warrior."
Boy/Male
Scandinavian
Bright.
Boy/Male
Danish, Finnish, German, Scandinavian, Swedish
Bright; Skillful
Boy/Male
French
From the alder grove.
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Boy/Male
Shakespearean
Much Ado About Nothing' A Headborough.
Male
English
English surname transferred to forename use, from a Norman baronial name VERE means "alder."
Male
German
German form of Latin Valentinus, VELTEN means "healthy, strong."
Surname or Lastname
English and Scottish (of Norman origin)
English and Scottish (of Norman origin) : habitational name from any of numerous places named in France named Vert or Le Vert.
Boy/Male
Hindu, Indian
Brave; Smart
Girl/Female
British, English
Beaver-stream
Surname or Lastname
English
English : see Fern.French : topographic name for someone who lived near a grove of alders, French verne, a word of Gaulish origin.
Male
English
Variant spelling of English Vern, VERNE means "place of alder trees."
Surname or Lastname
English
English : variant of Varney.
VERTEX MODEL
VERTEX MODEL
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Goddess Lakshmi
Boy/Male
Tamil
Hridayanath | ஹரதயநாத
Lord of the heart
Male
Greek
 Variant spelling of Greek Bakchos, BAKKHOS means "noisy, riotous."
Girl/Female
Indian
Place
Girl/Female
Arabic, Muslim
Virtues; Plural of Shamila
Boy/Male
British, English, Irish
Son of Cunotamus
Surname or Lastname
English
English : variant of Brookhouse.
Girl/Female
Teutonic
Noble wolf.
Boy/Male
Latin English French
Enduring.
Boy/Male
Gaelic
Dwells at the Crag.
VERTEX MODEL
VERTEX MODEL
VERTEX MODEL
VERTEX MODEL
VERTEX MODEL
imp. & p. p.
of Verse
n. sing. & pl.
A verse or verses. See Verse.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
n.
The outer or superficial part of an organ; as, the cortex or gray exterior substance of the brain.
n.
The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base.
n.
Any one of numerous species of small Turbellaria belonging to Vortex and allied genera. See Illustration in Appendix.
n.
The top, or crown, of the head.
v. i.
To tend downward; to bend; to slope; as, a hill verges to the north.
pl.
of Vertex
a.
Not in a state of contingency or suspension; fixed; as, vested rights; vested interests.
imp. & p. p.
of Verge
n.
An edible European marine fish (Sparus dentex, or Dentex vulgaris) of the family Percidae.
v. t.
To tell in verse, or poetry.
n.
A verse.
n.
One who carries a verge, or emblem of office.
pl.
of Vertex
v. i.
To make verses; to versify.
n.
The zenith, or the point of the heavens directly overhead.
n.
A stanza; a stave; as, a hymn of four verses.
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.