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MRI sequence simulation technique
In magnetic resonance imaging and nuclear magnetic resonance the extended phase graph (EPG) is a mathematical framework used to track how magnetization
Extended_phase_graph
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Matrix representation of a graph
determines a spectral layout in graph drawing. Graph-based signal processing is based on the graph Fourier transform that extends the traditional discrete Fourier
Laplacian_matrix
German chemist and medical physicist (born 1951)
and FSE (Fast Spin Echo). In 1991 Hennig published the so-called Extended Phase Graph(EPG)-method, which allows to calculate the signal intensity after
Jürgen_Hennig
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Spectral graph theory concept
spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are
Ramanujan_graph
Graphical representation
rhythms that extended beyond 24 hours and the existence of two oscillators within organisms. Actograms typically have a bar above the graph that indicates
Actogram
Algorithmic problem of finding non-crossing drawings
In graph theory, the planarity testing problem is the algorithmic problem of testing whether a given graph is a planar graph (that is, whether it can
Planarity_testing
In applied mathematics, a technique to find the shortest path
exploit properties of graphs representing road networks. The speed-up is achieved by creating shortcuts in a preprocessing phase which are then used during
Contraction_hierarchies
Magnetic resonance imaging technique
acquisition. Various models, such as Bloch Equations simulations and the extended phase graph formalism, have been employed to create these databases. More complex
Magnetic resonance fingerprinting
Magnetic_resonance_fingerprinting
Physical process of transition between basic states of matter
In physics, chemistry and biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another
Phase_transition
3D graphics computer library
succeeded by VulkanSceneGraph project, a Vulkan-based library. OpenSceneGraph is in maintenance phase since 2019. The OpenSceneGraph project was initiated
OpenSceneGraph
Clustering and community detection algorithm
refinement phase in which communities may be split to guarantee that all communities are well-connected. Consider, for example, the following graph: Three
Leiden_algorithm
Phase of a cycle
mechanics, the geometric phase (also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase) is a phase difference acquired over the
Geometric_phase
Type of data encoding
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency carrier wave. The
Phase-shift_keying
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
Type of discrete calculus
mathematics, 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
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
Measure of the structural complexity of a software program
Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program
Cyclomatic_complexity
Graph layout on multiple half-planes
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the
Book_embedding
Algorithm for finding shortest paths
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer
Dijkstra's_algorithm
Form taken by the network of interconnections of a circuit
of graph theory. Standard graph theory can be extended to deal with active components and multi-terminal devices such as integrated circuits. Graphs can
Circuit_topology_(electrical)
Graphical representation of energy flows in physical systems
A bond graph is a graphical representation of the energy flows through, and between physical dynamical systems including those in the electrical, mechanical
Bond_graph
Any planar graph can be subdivided by removing a few vertices
of the theorem has been improved, and it has been extended to certain classes of nonplanar graphs. Repeated application of the separator theorem produces
Planar_separator_theorem
History of a New York City Subway line
on the East Side of Manhattan, had been proposed since 1920. The first phase of the line, consisting of three stations on the Upper East Side, started
Construction of the Second Avenue Subway
Construction_of_the_Second_Avenue_Subway
Mathematical function, denoted exp(x) or e^x
third image shows the graph extended along the real x axis. It shows the graph is a surface of revolution about the x axis of the graph of the real exponential
Exponential_function
Mathematical model
thermodynamic phases occurring e.g. in technical alloy grades. Many of the results for continuum phase-field models have discrete analogues for graphs, just replacing
Phase-field_model
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
Mathematical model of ferromagnetism in statistical mechanics
that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all
Ising_model
Open problem in probability theory
d-regular trees. In Hutchcroft (2016), this result was extended to all quasi-transitive graphs of exponential growth. In Kozma & Nitzan (2024), the authors
Dying_percolation_conjecture
Important lemma in extremal graph theory
on to phase 2. Consider the set of vertices left to be embedded, which is precisely B, and the set of free spots ⋃b∈BFb(T). Form a bipartite graph between
Blow-up_lemma
Opposition of a circuit to a current when a voltage is applied
voltage. Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance,
Electrical_impedance
Graph in climate science
Hockey stick graphs present global or hemispherical mean global surface temperatures of the distant past, as shown by quantitative climate reconstructions
Hockey stick graph (global temperature)
Hockey_stick_graph_(global_temperature)
algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints,
List_of_algorithms
Italian professor, engineer and inventor
methodology used to analyze signals defined over a topological space, focusing on graphs, simplicial and cell complexes. This framework encompasses the conventional
Sergio_Barbarossa
Concept in network science
stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized
Stochastic_block_model
Plot using the dispersal of scattered dots to show the relationship between variables
A scatter plot, also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram, is a type of plot or mathematical diagram using
Scatter_plot
Radio technology devices
loss (dB) vs coupling (dB) for a dissipationless coupler is shown in the graph of figure 3 and the table below. Isolation of a directional coupler can
Power dividers and directional couplers
Power_dividers_and_directional_couplers
Cellular automaton
\mathbb {Z} ^{2}} , Lang and Shkolnikov introduced the extended sandpile model in 2019. The extended sandpile model is defined nearly exactly the same as
Abelian_sandpile_model
Free online crowdsourced encyclopedia
article can be "semi-protected" or "extended confirmed protected", meaning that only "autoconfirmed" or "extended confirmed" editors can modify it. A
Wikipedia
Gradual reduction of the use and production of fossil fuels
Fossil fuel phase-out is the proposed gradual global reduction of the use and production of fossil fuels to zero, to reduce air pollution, limit climate
Fossil_fuel_phase-out
Computational problem in graph theory
find an approximately optimal maximum flow but only work in undirected graphs. In 2013 James B. Orlin published a paper describing an O(|V||E|) algorithm
Maximum_flow_problem
Two-person zero-sum game
search game introduces: A search space X, which can be a Euclidean domain, a graph, or a more abstract state space. One or more searchers whose trajectory
Search_game
Ongoing COVID-19 viral pandemic in Madhya Pradesh, India
Authority (NDMA) and the MHA extended the lockdown for two weeks beyond 18 May, with additional relaxations. During this phase, the state government imposed
COVID-19 pandemic in Madhya Pradesh
COVID-19_pandemic_in_Madhya_Pradesh
Statistical mechanics model for phase transitions
known as Yang–Lee theory, is a scientific theory which seeks to describe phase transitions in large physical systems in the thermodynamic limit based on
Lee–Yang_theory
Fundamental trigonometric functions
circle. Using the unit circle definition has the advantage of drawing the graph of sine and cosine functions. This can be done by rotating counterclockwise
Sine_and_cosine
Polynomial-time algorithm for the assignment problem
described by formulating the problem using a bipartite graph. We have a complete bipartite graph G=(S,T;E) with n worker vertices (S) and n job vertices
Hungarian_algorithm
Tree representation of the abstract syntactic structure of source code
o(a1;…;an)∈𝒜[𝒳]s. Abstract semantic graph (ASG), also called term graph Composite pattern Control-flow graph Directed acyclic graph (DAG) Document Object Model
Abstract_syntax_tree
1999). "CyberGraphX 4". Amiga Format. No. 119. Future Publishing. p. 52. ISSN 0957-4867. amiga.resource.cx - Amiga Hardware Database - Phase 5 Digital Products
Retargetable_graphics
years" before it was released to the public in 2004. Since Gmail's beta phase, it's gained new features and changes. Google Workspace enhancements are
History_of_Gmail
Quarantine effort in response to the COVID-19 pandemic in India
the lockdown would be further extended until 30 June for only the containment zones. Services would be resumed in a phased manner starting from 8 June.
COVID-19_lockdown_in_India
Optimization problem
the sparse original graph into a complete graph. For each pair of vertices i and j, there exists an arc (i,j) of the complete graph whose cost is written
Vehicle_routing_problem
Family of protocols for solving consensus
in this quorum is a read quorum for the prepare phase of the next rounds. Paxos may also be extended to support arbitrary failures of the participants
Paxos_(computer_science)
Concurrency control technique for databases
of Extended CO (ECO) below: Global transactions' voting order must follow the conflict graph order with vote blocking when order relation (graph path)
Commitment_ordering
oscillator phase, defined by Γ(ψ)=12π∫02πZ(ψ+η)⋅g(ηΩ)dη. The graph of this function Γ(ψ) can be shown to exhibit the dynamics of the approximated phase model
Phase_reduction
American physicist and climatologist
reconstruction over the past 1,000 years (MBH99), which was dubbed the "hockey stick graph" because of its shape. He was one of eight lead authors of the "Observed
Michael_E._Mann
Settlement without third party involvement
satisfactorily for graphs up to 500 vertices (running time within a few hours) with technology from 1992. For larger graphs, the two-phase heuristic achieved
Collaborative_finance
Planning technique
makes the communication and integration easier. Graphs: A technology roadmap can also be expressed as a graph, usually one for each of the sub layers. (e
Technology_roadmap
Ongoing COVID-19 viral pandemic in Pennsylvania, United States
Governor Wolf extended the stay-at-home order until June 4 for counties in the red phase. On May 8, 24 counties entered the yellow phase, allowing some
COVID-19 pandemic in Pennsylvania
COVID-19_pandemic_in_Pennsylvania
Application platform accessing Facebook's social network
interfaces and tools which enable developers to integrate with the open "social graph" of personal relations and other things like songs, places, and Facebook
Facebook_Platform
Logic problem, AND of pairwise ORs
type of directed graph, the implication graph, which expresses the variables of an instance and their negations as vertices in a graph, and constraints
2-satisfiability
Conclusion of the human pregnancy
latent and active phases, where the latent phase is sometimes included in the definition of labour, and sometimes not. The latent phase is generally defined
Childbirth
Analog of the continuous Laplace operator
operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices)
Discrete_Laplace_operator
Frequency of a chirp pulse
waveforms where the time-bandwidth product is large. The full line on the graph of the adjacent figure shows results for linear chirps. It shows, for example
Chirp_spectrum
Condensed matter physics model involving only closed loops
In condensed matter physics, a string-net is an extended object whose collective behavior has been proposed as a physical mechanism for topological order
String-net_liquid
Ongoing COVID-19 viral pandemic in Punjab, India
Phase 1a Health Minister Balbir Singh Sidhu announced around 1.60 lakh health workers in Punjab will receive a COVID-19 vaccine in the first phase, after
COVID-19 pandemic in Punjab, India
COVID-19_pandemic_in_Punjab,_India
sequences to generate highly phased contig assemblies. Three different tools were used to construct the pangenome graph: Minigraph: It represents a methodology
Human_Pangenome_Reference
algebra is mostly done using graphs, using points, lines, areas etc. to represent various parameters of problems. Graphing calculators can take inputs
Mathematical_visualization
Part of the Islamic conquest of Persia
Muslims conquered Khorasan in the last phase of their conquest of Sasanian Persia. The conquest was followed by the Islamization of the region. In 642
Muslim_conquest_of_Khorasan
ISO standard
CAD systems for import and export. In the second phase the capabilities of STEP were widely extended, primarily for the design of products in the aerospace
ISO_10303
Symmetry between bosons and fermions
general form, including those with an extended number of the supergenerators and central charges. This extended super-Poincaré algebra paved the way for
Supersymmetry
Concept in physics
or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise
Self-organized_criticality
Mathematical parameter in percolation theory
Non-equilibrium phase transitions, Vol. 1: Absorbing phase transitions. Springer, Dordrecht. Janssen, H. K. (1981). "On the nonequilibrium phase transition
Percolation critical exponents
Percolation_critical_exponents
Electricity converter
one to a phase on the top row and one (from a different phase) on the bottom row. The two conducting valves connect two of the three AC phase voltages
HVDC_converter
Method to control electric motors
variable-frequency drive (VFD) control method in which the stator currents of a three-phase AC motor (like for example BLDC) are identified as two orthogonal components
Field-oriented_control
American musical duo
and Garfunkel assumed the name Tom & Jerry; Garfunkel named himself Tom Graph, a reference to his interest in mathematics, and Simon named himself Jerry
Simon_&_Garfunkel
Numerical analysis of EEG data
with new focus on shared activity between rhythms including phase synchrony (coherence, phase lag) and magnitude synchrony (comodulation/correlation, and
Quantitative electroencephalography
Quantitative_electroencephalography
Coordinates comprising a distance and an angle
then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r. Note that, in contrast to Cartesian coordinates
Polar_coordinate_system
Audio effect
is plotted on a linearly-scaled graph, the trace resembles a comb, and so is called a comb filter. Moiré pattern Phaser (effect) Martin, George; Pearson
Flanging
Method of microscopic imaging
using a pinhole aperture in a piece of cardboard. In the graphs, the hue represents the phase, and the modulus represents the luminance. (a) shows a single
Ptychography
Law of thermodynamics for vapour pressure of a mixture
correction for interactions in the liquid phase between the different molecules. This modified or extended Raoult's law is then written as yiϕp,ip=xiγipi⋆
Raoult's_law
Square root of the mean square
Alternatively, for waveforms that are perfectly positively correlated, or "in phase" with each other, their RMS values sum directly. The RMS of an alternating
Root_mean_square
Imaging technique
3D imaging capability of Digital Holography in amplitude and phase it is possible to extend the depth of focus in microscopy. The digital analysis of a
Digital_holography
Describes how neurons transmit electric signals
exist. Because there are four state variables, visualizing the path in phase space can be difficult. Usually two variables are chosen, voltage V m (
Hodgkin–Huxley_model
Parameter describing physics near critical points
Reissner–Nordström AdS black hole in extended phase space. The most accurately measured value of α is −0.0127(3) for the phase transition of superfluid helium
Critical_exponent
Plan to immunize against COVID-19
first phase, the objective was reducing mortality and severe case incidence rates from COVID-19, as well as protecting health workers. The second phase was
COVID-19 vaccination in Colombia
COVID-19_vaccination_in_Colombia
in Asia are balanced by retirements of aging plants and nuclear reactor phase-outs. Global nuclear electricity generation in 2012 was at its lowest level
Nuclear energy policy by country
Nuclear_energy_policy_by_country
Chinese mathematician (born 1968)
learning, and inference." Zhu has extended the and-or graph models to the spatial, temporal, and causal and-or graph (STC-AOG) to express the compositional
Song-Chun_Zhu
History of research by Augustin-Jean Fresnel
and Fresnel Integrals". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards. Applied Mathematics
Fresnel's_physical_optics
Motherboard and power supply configuration
ATX (Advanced Technology Extended) is a motherboard and power supply form factor and configuration specification developed by Intel. It aimed to improve
ATX
Speed and direction of a motion
one-dimensional case it can be seen that the area under a velocity vs. time (v vs. t graph) is the displacement, s. In calculus terms, the integral of the velocity
Velocity
Property of an intermediate representation in a compiler
RVM, uses extended Array SSA, an extension of SSA that allows analysis of scalars, arrays, and object fields in a unified framework. Extended Array SSA
Static_single-assignment_form
Equivalence of average-case and expected complexity
the evasiveness of graph properties, the number of tests of the adjacency of pairs of vertices needed to determine whether a graph has a given property
Yao's_principle
Characteristic of an optical system
optical transfer function with phase ignored) gives the true measure of lens performance, and is represented by a graph of amplitude against spatial frequency
Optical_transfer_function
British record store
Voice-o-Graph, inaugurating the series with a performance from Frank Turner. Jacaranda's first period of expansion began with the opening of Phase One in
Jacaranda_Records
Generalized mathematical function
If f is an ordinary function, it is a multivalued function by taking its graph Γf = {(x,f(x)) : x∈X}. They are called single-valued functions to distinguish
Multivalued_function
16-element matrix group
16-element matrix group, consisting of the 4 Pauli matrices each with 4 possible phase factors. The n-qubit Pauli group is a 4n+1-element group consisting of tensor
Pauli_group
Consensus algorithm
Algorithm (Extended Version)" (PDF). raft.github.io. Retrieved 2025-10-01. "In Search of an Understandable Consensus Algorithm (Extended Version)" (PDF)
Raft_(algorithm)
Replacing subterm in a formula with another term
reformulated for HRSs as well. Graph rewrite systems are another generalization of term rewrite systems, operating on graphs instead of (ground-) terms /
Rewriting
"Mahō no Tokei" (Japanese: まほうのとけい) November 13, 1980 (1980-11-13) 466 "A Graph that Never Lies" Transliteration: "Gurafu wa Uso o Tsukanai" (Japanese:
List of Doraemon (1979 TV series) episodes (1979–1986)
List_of_Doraemon_(1979_TV_series)_episodes_(1979–1986)
Indian state election
Indian state of Uttar Pradesh from 10 February to 7 March 2022 in seven phases to elect all 403 members for the 18th Uttar Pradesh Legislative Assembly
2022 Uttar Pradesh Legislative Assembly election
2022_Uttar_Pradesh_Legislative_Assembly_election
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